Gradient Method

This paper considers semiblind channel estimation and data detection for orthogonal frequency-division multiplexing (OFDM) over frequency-selective fading channels. We show that the samples of an OFDM symbol are jointly complex Gaussian distributed, where the mean and covariance are determined by the locations and values of fixed pilot symbols. We exploit this distribution to derive a novel maximum-likelihood (ML) semiblind gradient-descent channel estimator. By exploiting the channel impulse response (CIR) statistics, we also derive a semiblind data detector for both Rayleigh and Ricean fading channels. Furthermore, we develop an enhanced data detector, which uses the estimator error statistics to mitigate the effect of channel estimation errors. Efficient implementation of both the semiblind and the improved data detectors is provided via sphere decoding and nulling-canceling detection. We also derive the Cramér-Rao bound (CRB) and design optimal pilots by minimizing the CRB. Our proposed channel estimator and data detector exhibit high bandwidth efficiency (requiring only a few pilot symbols), achieve the CRB, and also nearly reach the performance of an ideal reference receiver.

The paper considers the problem of optimal control of the process of thermal conductivity of a homogeneous disk (ball). An optimization problem is posed for a one-dimensional parabolic type equation with a mixed-type boundary condition. The goal of the control is to bring the temperature distribution in the disk (ball) to a given distribution in a finite time. To solve this problem, an algorithm is proposed that is based on the gradient method. The object of the study is the optimal control problem for a parabolic boundary value problem. Using the discretization of the original continuous differential problem, difference equations are obtained for which a numerical solution algorithm is proposed. Difference approximation of a differential problem is performed using an implicit scheme, which allows to increase the speed of calculations and provides the specified accuracy of calculation for a smaller number of iterations. An approximate solution of a parabolic equation is constructed using the one-dimensional sweep method. Using differentiation of the functional, an expression for the gradient of the objective functional is obtained. In this paper, it was possible to reduce the multidimensional heat conduction problem to a one-dimensional one, due to the assumption that the desired solution is symmetric. A formula is obtained for calculating the variation of a quadratic functional that characterizes the deviation of the current temperature distribution from the given one. The flowcharts and implementations of the algorithm are presented in the form of Matlab scripts, which clearly demonstrate the process of thermal conductivity and show the computation and application of optimal control in dynamics.

In this paper we consider optimization problems de ned by a quadratic objective function and a nite number of quadratic inequality constraints. Given that the objective function is bounded over the feasible set, we present a comprehensive study of the conditions under which the optimal solution set is nonempty, t h us extending the so-called Frank-Wolfe theorem. In particular, we rst prove a general continuity result for the solution set de ned by a system of convex quadratic inequalities. This result implies immediately that the optimal solution set of the aforementioned problem is nonempty when all the quadratic functions involved are convex. In the absence of the convexity of the objective function, we give examples showing that the optimal solution set may be empty either when there are two or more convex quadratic constraints, or when the Hessian of the objective function has two or more negative eigenvalues. In the case when there exists only one convex quadratic inequality constraint together with other linear constraints, or when the constraint functions are all convex quadratic and the objective function is quasi-convex thus allowing one negative eigenvalue in its Hessian matrix, we prove that the optimal solution set is nonempty.

In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we introduce a new notion of -stationarity, which is suitable for the structured problem under consideration. We then propose two types of first-order algorithms for the model based on the proximal conditional-gradient (CG) method and the proximal gradient-projection method respectively. If the nonconvex objective function is in the form of mathematical expectation, we then discuss how to incorporate randomized sampling to avoid computing the expectations exactly. For the general block optimization model, the proximal subroutines are performed for each block according to either the blockcoordinate-descent (BCD) or the maximum-block-improvement (MBI) updating rule. If the gradient of the nonconvex part of the objective f satisfies ∇f (x) -∇f (y) q ≤ M x -y δ p where δ = p/q with 1/p + 1/q = 1, then we prove that the new algorithms have an overall iteration complexity bound of O(1/ q ) in finding an -stationary solution. If f is concave then the iteration complexity reduces to O(1/ ). Our numerical experiments for tensor approximation problems show promising performances of the new solution algorithms.

Objective: We assess whether socioeconomic status (SES) is associated with basal levels of cortisol and catecholamines and determine if any association between SES and these hormones can be explained (is mediated) by behavioral, social, and emotional differences across the SES gradient. Methods: One hundred ninety-three adult subjects, including men and women and whites and African-Americans, provided 24-hour urine catecholamine samples on each of 2 days and seven saliva cortisol samples on each of 3 days beginning 1 hour after wakeup and ending 14 to 16 hours later. Values for both hormones were averaged across days to obtain basal levels. Results: Lower SES (income and education) was associated with higher levels of cortisol and epinephrine and marginally higher levels of norepinephrine. These associations were independent of race, age, gender, and body mass. Low SES was also associated with a greater likelihood of smoking, of not eating breakfast, and with less diverse social networks. Further analyses provided evidence consistent with the hypothesis that these behavioral and social variables mediate the link between SES and the three stress hormones. Conclusions: Lower SES was associated in a graded fashion with higher basal levels of cortisol and catecholamines. These associations occurred independent of race, and the data were consistent with mediation by health practices and social factors.

A simple, sensitive, and accurate chromatography (RP-HPLC) method for simultaneous estimation of Ciprofloxacin, Ofloxacin, and Marbofloxacin in their combined pharmaceutical dosage form or individually. The HPLC separation was achieved on a Hypersil (C18, 150 mm × 4.6 mm, 5 μm particle size) analytical column or equivalent. A mixture of triethanolamine (1 %), acetonitrile (80 %), and water was used as the mobile phase, with a flow rate of 1.2 mL /min and a detector wavelength of 280 nm at ambient temperature. In the HPLC method, the retention times of Ciprofloxacin, Ofloxacin, and Marbofloxacin were found to be 1.854, 2.480, and 4.688 min, respectively, and linearity was obtained in the range of 25-80 µg/mL for Ciprofloxacin, Ofloxacin, and Marbofloxacin. The correlation coefficient for the method was greater than 0.999. The RP-HPLC method validation parameter lay within its acceptance criteria as per the ICHq2 (R1) guideline. Hence, it can be successfully used for routine analysis of Ciprofloxacin, Ofloxacin, and Marbofloxacin in raw material or pharmaceutical dosage forms.

A simple, sensitive, and accurate chromatographic (RP-HPLC) method for simultaneous estimation of norfloxacin, levofloxacin, and moxifloxacin in their combined. Pharmaceutical dosage forms or individually. The HPLC separation was achieved on a Hypersil (C18, (150 mm x 4.6 mm,5 μm particle size) analytical column or equivalent. A Mixture of triethanolamine 1%: acetonitrile 80 % was used as the suitable mobile phase, at a flow rate of 1.2 mL/min and detector wavelength at 280 nm at ambient temperature (25 °C). In the HPLC method, the retention time of norfloxacin, levofloxacin, and moxifloxacin was found to be 1.854, 2.480, and 4.688 min, respectively, and the linearity of the method was obtained in the range from 25 to 80 µg/mL for norfloxacin, levofloxacin, and moxifloxacin. The Correlation coefficient for the method was greater than 0.999 RP-HPLC method validation parameter lay within its acceptance criteria as per the ICHq2 (R1) guideline Validation of analytical procedures. Hence it can be successfully used for routine analysis of norfloxacin, levofloxacin, and moxifloxacin in raw material or pharmaceutical dosage forms.

Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by . Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheffé polynomials (Scheffé 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of . If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex.

The conjugated gradient methods can solve smooth functions with large-scale variables in the specified number of iterations for that they are highly important methods compared to concerning other iterative methods. In this paper, we propose two new conjugate gradient methods, namely the PMDL-1 and PMDL-2. However, for non-smooth functions, which are called conjugate gradient-free derivative methods depending on the projection technique. The two methods give great results compared to the basic PDL method. Moreover, we provide theorems that prove the global convergence between these two methods.

Intelligent algorithms are among the most suitable methods for practical applications, as well as conjugate gradient algorithms (CGAs), which are very useful in solving multidimensional optimization problems. Therefore, combining optimization methods with heuristic algorithms is an exciting research idea to enhance the efficiency of solutions. This paper discusses the suitability of a new parameter in the conjugate gradient algorithm with the mayfly algorithm for various optimization problems. The proposed strategy is characterized by its high ability to reach the optimal point consistently, thanks to the careful choice of the step size resulting from the combination of the two methods. We also prove the global convergence of the algorithm based on basic assumptions, and finally the new method shows superior performance when compared with other algorithms in the same field.

This paper proposes and develops new linesearch methods with inexact gradient information for finding stationary points of nonconvex continuously differentiable functions on finite-dimensional spaces. Some abstract convergence results for a broad class of linesearch methods are established. A general scheme for inexact reduced gradient (IRG) methods is proposed, where the errors in the gradient approximation automatically adapt with the magnitudes of the exact gradients. The sequences of iterations are shown to obtain stationary accumulation points when different stepsize selections are employed. Convergence results with constructive convergence rates for the developed IRG methods are established under the Kurdyka-Lojasiewicz property. The obtained results for the IRG methods are confirmed by encouraging numerical experiments, which demonstrate advantages of automatically controlled errors in IRG methods over other frequently used error selections.

Introduction Distillers grains are a coproduct of the biofuel production process and have been used as animal feed for nearly a century. Due to an increased interest in alternative fuels coupled with the rising cost of corn and soybean meal, the distillers grains industry has witnessed significant growth. When present in livestock rations, distillers grains are an excellent source of energy, protein, and essential minerals that provide three times the amount of nutrients available from unprocessed grain.1 Because the nutritional composition of dried distillers grains with solubles (DDGS) can vary from batch to batch, the distillery industry is interested in determining DDGS composition to properly formulate a nutritionally balanced diet for the animal feed industry.2

The dynamical behavior of the PBL (Planetary Boundary Layer) has a direct effect on the air quality and on the boundary layer parameterization schemes used in local, regional and global models. Active remote sensing systems such as LIDARs (Light Detection and Ranging) use aerosols of the atmosphere as tracers for identification of atmospheric state determined by convective activity, turbulence or

The paper considers a parametric optimization problem for the bar structures formulated as nonlinear programming task, where the purpose function and non-linear constraints of the mathematical model are continuously differentiable functions of the design variables. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the parametric optimization problem. A discretization technique for the design variables that should vary discretely has been proposed. The discretization of the optimal design solution obtained in the continuous space of the design variables is performed by the purposefully selecting discrete points around the point of the continuous optimum. The comparison of the optimization results presented by the paper demonstrates that improved gradient method together with proposed discretization technique for the discrete design variables converges to better...

The paper considers parametric optimisation problems for the bar structures formulated as non-linear programming tasks. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the parametric optimisation problem. Equivalent Householder transformations of the resolving equations of the method have been proposed. They increase numerical efficiency of the algorithm developed based on the method under consideration. Additionally, proposed improvement for the gradient-based method also consists of equivalent Givens transformations of the resolving equations. They ensure acceleration of the iterative searching process in the specified cases described by the paper due to decreasing the amount of calculations. The comparison of the optimisation results of truss structures presented by the paper confirms the validity of the optimum solutions obtained using proposed improvement of the gradient-based method. The efficiency of the propoced improvement of the gradient-based method has been also confirmed taking into account the number of iterations and absolute value of the maximum violation in the constraints.

In this paper parametric optimization of plane two-hinged steel truss with hollow structural members has been considered. Cross sectional sizes of circular hollow brace and chord members and node coordinates of steel truss have been considered as design variables. The system of constraints included stresses and buckling checks for each structural member as well as displacements checks for defined structural nodes. A set of technological requirements have been also integrated to the system of constraints. The minimum structural weight and minimum construction budget was considered as the purpose function. An update gradient method has been proposed in order to solve the parametric optimization task. Suggested optimization technique has been implemented with elaborated software OPTCAD. Numerical example presented by paper has been demonstrated the effectiveness of the proposed optimization methodology.

The conjugate gradient methods are one of the most important techniques used to address problems involving minimization or maximization, especially nonlinear optimization problems with no constraints at all. That is because of their simplicity and low memory needed. They can be applied in many areas, such as economics, engineering, neural networks, image restoration, machine learning, and deep learning. The convergence of Fletcher-Reeves (FR) conjugate gradient method has been established under both exact and strong Wolfe line searches. However, it is performance in practice is poor. In this paper, to get good numerical performance from the FR method, a little modification is done. The global convergence of the modified version has been established for general nonlinear functions. Preliminary numerical results show that the modified method is very efficient in terms of number of iterations and CPU time.

Nonlinear Conjugate Gradient (CG) methods are extensively used for solving large-scale unconstrained optimization problems. Numerous of studies constructed scales and modifications have been conducted recently to improve (CG) methods. In this paper, a simple modified by its conjugate gradient method was proposed. In addition to, established global convergence property and sufficient descent condition, under Strong Wolfe line search. Numerical result shows that the proposed formula is competitive when compared to other well-known (CG) parameters.

Nonlinear conjugate gradient methods for unconstrained optimization problems are used in many aspects of theoretical and applied sciences. They are iterative methods, so at any iteration a step length is computed using a method called line search. In most cases, the sufficient descent condition plays an important role to prove the global convergence of a conjugate gradient method. Due to its outperformance in practical computation, the Polak-Ribière-Polyak (PRP) conjugate gradient method is widely used for solving nonlinear unconstrained optimization problems. However, the sufficient descent condition of PRP has not established without line search yet. In this study, we established the sufficient descent condition without line search based on the conditions 0 < k PRP   k FR and 1 < k PRP k FR , where 0 <  < 1 and  > 1. As a result, we found that under certain conditions, the sufficient descent condition is satisfied when the PRP implemented without line search.

Nonlinear conjugate gradient methods for unconstrained optimization problems are used in many aspects of theoretical and applied sciences. They are iterative methods, so at any iteration a step length is computed using a method called line search. In most cases, the sufficient descent condition plays an important role to prove the global convergence of a conjugate gradient method. Due to its outperformance in practical computation, the Polak-Ribière-Polyak (PRP) conjugate gradient method is widely used for solving nonlinear unconstrained optimization problems. However, the sufficient descent condition of PRP has not established without line search yet. In this study, we established the sufficient descent condition without line search based on the conditions 0 < k PRP   k FR and 1 < k PRP k FR , where 0 <  < 1 and  > 1. As a result, we found that under certain conditions, the sufficient descent condition is satisfied when the PRP implemented without line search.

Variable metric proximal gradient (VM-PG) is a widely used class of convex optimization method. Lately, there has been a lot of research on the theoretical guarantees of VM-PG with different metric selections. However, most such metric selections are dependent on (an expensive) Hessian, or limited to scalar stepsizes like the Barzilai-Borwein (BB) stepsize with lots of safeguarding. Instead, in this paper we propose an adaptive metric selection strategy called the diagonal Barzilai-Borwein (BB) stepsize. The proposed diagonal selection better captures the local geometry of the problem while keeping perstep computation cost similar to the scalar BB stepsize i.e. O(n). Under this metric selection for VM-PG, the theoretical convergence is analyzed. Our empirical studies illustrate the improved convergence results under the proposed diagonal BB stepsize, specifically for ill-conditioned machine learning problems for both synthetic and real-world datasets.

This thesis presents applications and an analysis of various adaptive control augmentation schemes to various baseline flight control systems of an air to ground guided missile. The missile model used in this research has aerodynamic control surfaces on its tail section. The missile is desired to make skid to turn maneuvers by following acceleration commands in the pitch and yaw axis, and by keeping zero roll attitude. First, a linear quadratic regulator baseline autopilot is designed for the control of the missile acceleration in pitch axis at a single point in the flight envelope. This baseline autopilot is then augmented with a Direct Model Reference Adaptive Control (D-MRAC) scheme using Neural Networks for parameter estimation, and an L1 Adaptive Control scheme. Using the linearized longitudinal model of the missile at the design point, simulations are performed to analyze and demonstrate the performance of the two adaptive augmentation schemes. By injecting uncertainties to the plant model, the effects of adaptive augmentations on the linear baseline autopilot are examined. v Secondly, a high fidelity simulation software of the missile is used in order to analyze the performance of the adaptive augmentations in 6 DoF nonlinear flight simulations. For the control of the missile in three axis, baseline autopilots are designed using dynamic inversion at a single point in the flight envelope. A linearizing transformation is employed during the inversion process. These coarsely designed baseline autopilots are augmented with L1 adaptive control elements. The performance of the adaptive control augmentation system is tested in the presence of perturbations in the aerodynamic model and increase in input gain, and the simulation results are presented.

In this paper, we will first study the existence and uniqueness of the solution for a one dimensional Inverse Heat Conduction Problem (IHCP) via an auxiliary problem. Then a stable numerical method consists of the zeroth-, first-and second-order Tikhonov regularization method to the matrix form of Duhamel's principle for solving this IHCP by using noisy data is presented. The inverse problem has a unique solution, but this solution is unstable hence the problem is ill-posed. This instability is overcome using the Tikhonov regularization method with the gcv criterion for the choice of the regularization parameter. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition (SVD) method.

In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the phase-locked solutions, the rotating waves, we provide a rigorous stability analysis. This analysis shows a strong dependence of their stability on the coupling structure and the wavenumber which is a remarkable difference to an all-to-all coupled network. Despite the fact that solitary states have been observed in a plethora of dynamical systems, the mechanisms behind their emergence were largely unaddressed in the literature. Here, we show how solitary states emerge due to the adaptive feature of the network and classify several bifurcation scenarios in which these states are created and stabilized.

Conjugate gradient (CG) methods are a popular family of iterative algorithms to solve large-scale nonlinear optimization problems due to appropriate features such as no need to calculate the second-order derivatives, low storage and computation, and suitable convergence rate. In this paper, based on the Hestenes-Stiefel method and Conjugate Descent method, new hybrid conjugate gradient method (named hHC method) is proposed for unconstrained optimization. The new method generates a descent direction independently of any line search and possesses good convergence properties under the strong Wolfe line search conditions. Numerical tests demonstrate the effectiveness of the new hybrid conjugate gradient method when compared to certain existing methods in view of the Dolan and Moré performance profile. Furthermore, the proposed algorithm was extended to solve problem of mode function.

Conjugate gradient methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems as they do not require the storage of any matrices. In order to obtain a theoretically effective and numerically efficient method, two modified conjugate gradient methods (called the MCB1 and MCB2 methods) are proposed. In which the coefficientβkin the two proposed methods is inspired by the structure of the conjugate gradient parameters in some existing conjugate gradient methods. Under the strong Wolfe line search, the sufficient descent property and global convergence of the MCB1 method are proved. Moreover, the MCB2 method generates a descent direction independently of any line search and produces good convergence properties when the strong Wolfe line search is employed. Preliminary numerical results show that the MCB1 and MCB2 methods are effective and robust in minimizing some unconstrained optimization problems and each of these modif...

Crop-water production functions (CWPFs) are a useful tool for irrigation planning, but derivation of CWPFs by field experimentation is expensive, and traditional analytical techniques are not well suited to derivation of CWPFs. Physiologically based crop models provide a useful tool for simulation of agricultural experiments, but they have not been extensively applied to the task of CWPF determination. A new algorithm type based upon differential crop yield response to irrigation (''yield-irrigation gradients'' [YIG]) is presented that uses these crop models to determine planning-level irrigation schedules and CWPFs. Three specific algorithms are developed within this type, varying in complexity, performance, and computational costs. Performance of the YIG methods is compared against a standard reference evapotranspiration method. In particular, the randomized iterative YIG (RIYIG) algorithm provides near-optimal results but at the highest computational costs of all the methods specified. All of the techniques presented have general applicability and are not limited to any one crop or location.

3 . The images were obtained at two different echo times (TE:s) using a dual echo, multi slice, spoiled, fast gradient echo pulse sequence. The first echo was obtained using TE1 = 2.3 ms with the water and fat signals out of phase, and the second using TE2 = 4.6 ms with the water and fat in phase. The repetition

A real valued function f defined on a convex K is an approximately convex function iff it satisfies A thorough study of approximately convex functions is made. The principal results are a sharp universal upper bound for lower semi-continuous approximately convex functions that vanish on the vertices of a simplex and an explicit description of the unique largest bounded approximately convex function E vanishing on the vertices of a simplex. A set A in a normed space is an approximately convex set iff for all a, b ∈ A the distance of the midpoint (a + b)/2 to A is ≤ 1. The bounds on approximately convex functions are used to show that in R n with the Euclidean norm, for any approximately convex set A, any point z of the convex hull of A is at a distance of at most [log 2 (n -1)] + 1 + (n -1)/2 [log 2 (n-1)] from A. Examples are given to show this is the sharp bound. Bounds for general norms on R n are also given.

The purpose of Conjugate gradient method for optimization is used
to solve a linear system, or equivalently, optimize a quadratic con
vex function. The algorithm can be adapted for optimizing general
differentiable functions and can be improved by considering vari
ations of direction coefficient βk. Numerical experiments showed
that the method converges to the approximated solutions and close
to the best choice of the formula for a given problem. Due to
jumping (not all consecutive descent directions or gradients are
conjugated in orthogonal) or susceptible to jumping or loss of de
scent or convergence failure, no fundamental formula for βk exists
. All their βk formulas consists of descent directions and gradients.
To find formula for βk, it is not easy without descent directions
or gradients. Although we have got different formulae for conju
gate parameter βk to get the best approximated solutions, only
improve and give direction for the future work. This project work
verifies various fundamental conjugate parameters for solving un
constrained nonlinear optimization problem.
keywords: -conjugacy,descent direction, search direction, Wolfe
condition, linear system equation, unconstrained nonlinear
optimization problem.

Настоящая статья посвящена некоторым адаптивным методам первого порядка для оптимизационных задач с относительно сильно выпуклыми функционалами. Недавно возникшее в оптимизации понятие относительной сильной выпуклости существенно расширяет класс выпуклых задач посредством замены в определении евклидовой нормы расстоянием в более общем смысле (точнее -расхождением или дивергенцией Брегмана). Важная особенность рассматриваемых в настоящей работе классов задач -обобщение стандартных требований к уровню гладкости целевых функционалов. Точнее говоря, рассматриваются относительно гладкие и относительно липшицевые целевые функционалы. Это может позволить применять рассматриваемую методику для решения многих прикладных задач, среди которых можно выделить задачу о нахождении общей точки системы эллипсоидов, а также задачу бинарной классификации с помощью метода опорных векторов. Если целевой функционал минимизационной задачи выпуклый, то условие относительной сильной выпуклости можно получить посредством регуляризации. В предлагаемой работе впервые предложены адаптивные методы градиентного типа для задач оптимизации с относительно сильно выпуклыми и относительно липшицевыми функционалами. Далее, в статье предложены универсальные методы для относительно сильно выпуклых задач оптимизации. Указанная методика основана на введении искусственной неточности в оптимизационную модель. Это позволило обосновать применимость предложенных методов на классе относительно гладких, так и на классе относительно липшицевых функционалов. При этом показано, как можно реализовать одновременно адаптивную настройку на значения параметров, соответствующих как гладкости задачи, так и введенной в оптимизационную модель искусственной неточности. Более того, показана оптимальность оценок сложности с точностью до умножения на константу для рассмотренных в работе универсальных методов градиентного типа для обоих классов относительно сильно выпуклых задач. Также в статье для задач выпуклого программирования с относительно липшицевыми функционалами обоснована возможность использования специальной схемы рестартов алгоритма зеркального спуска и доказана оптимальная оценка сложности такого алгоритма. Также приводятся результаты некоторых вычислительных экспериментов для сравнения работы предложенных в статье методов и анализируется целесообразность их применения. Ключевые слова: адаптивный метод, относительно сильно выпуклый функционал, относительно гладкий функционал, относительно липшицев функционал, оптимальный метод, зеркальный спуск Работа выполнена при поддержке Российского научного фонда, проект 21-71-30005.

Transformations of the form A + E'FAg2 are investigated that transform Toeplitz and Toeplitz-plus-Hankel matrices into generalized Cauchy matrices. 'Zi and @a are matrices related to the discrete Fourier transformation or to various real trigonometric transformations. Combining these results with pivoting techniques, in paper II algorithms for Toeplitz and Toeplitz-plus-Hankel systems will be presented that are more stable than classical algorithms.

Finding the sparse solution to under-determined or ill-condition equations is a fundamental problem encountered in most applications arising from a linear inverse problem, compressive sensing, machine learning and statistical inference. In this paper, inspired by the reformulation of the ?1-norm regularized minimization problem into a convex quadratic program problem by Xiao et al. (Nonlinear Anal Theory Methods Appl, 74(11), 3570-3577), we propose, analyze, and test a derivative-free conjugate gradient method to solve the ?1-norm problem arising from the reconstruction of sparse signal and image in compressive sensing. The method combines the MLSCD conjugate gradient method proposed for solving unconstrained minimization problem by Stanimirovic et al. (J Optim Theory Appl, 178(3), 860-884) and a line search method. Under some mild assumptions, the global convergence of the proposed method is established using the backtracking line search. Computational experiments are carried out t...

Engineering optimization often deals with very large search spaces which are highly constrained by nonlinear equations that couple the continuous variables. In this contribution the development of a memetic algorithm (MA) for global optimization in the solution of a problem in the chemical process engineering domain is described. The combination of an evolutionary strategy and a local solver based on the general reduced gradient method enables the exploitation of a significant reduction in the search space and of the ability of local mathematical programming solvers to efficiently handle large continuous problems containing equality constraints. The global performance of the MA is improved by the exclusion of regions that are defined by approximations of the basins of attraction of the local optima. The MA is compared to the combination of a scatter search based multi-start heuristic using OQNLP and the local solver CONOPT.

A mobile platform mounted with omnidirectional vision sensor (ODVS) can be used to monitor large areas and detect interesting events such as independently moving persons and vehicles. To avoid false alarms due to extraneous features, the image motion induced by the moving platform should be compensated. This paper describes a formulation and application of parametric egomotion compensation for an ODVS. Omni images give 360 • view of surroundings but undergo considerable image distortion. To account for these distortions, the parametric planar motion model is integrated with the transformations into omni image space. Prior knowledge of approximate camera calibration and camera speed is integrated with the estimation process using a Bayesian approach. Iterative, coarse-to-fine, gradient-based estimation is used to correct the motion parameters for vibrations and other inaccuracies in prior knowledge. Experiments with a camera mounted on various types of mobile platforms demonstrate successful detection of moving persons and vehicles.

Nonmonotone spectral gradient (NSG) techniques are considered for unconstrained optimization of differentiable functions. They combine a nonmonotone step length strategy, that is based on the Grippo-Lampariello-Lucidi nonmonotone line search, with the spectral gradient choice of steplength. In this paper, we present a hybrid nonmonotone spectral gradient method. In each iteration after finding an acceptable point by NSG method, we employ an extrapolation step to find a even better point by using particle swarm optimization. Through specific assumptions, we prove the global convergence of our proposed algorithm Keywords Barzilai-Borwein method • Nonmonotone line search • Particle swarm optimization B Halima Lakhbab

We propose a practical approach to spin-polarized systems within the van der Waals density functional (vdW-DF). The method was applied to a gas phase oxygen molecule and a parallel (H-type) pair of oxygen molecules. It was found that vdW-DF improves the equilibrium distance and binding energy. In particular, one type of vdW-DF can describe such systems reasonably well. The van der Waals interaction has been confirmed to have an energy comparable to the magnetic one, while emerging at a distance rather longer than the latter.

Anti-jamming techniques are critical to maintain the integrity and functionality of GPS systems in various applications. One of the major problems with existing array-based antijamming GPS receivers is the errors introduced in the carrier phase, affecting the GPS solution. In this letter, we propose a novel anti-jamming GPS receiver structure that preserves the GPS signal phase continuity. The effectiveness of the proposed technique is verified by simulation results.

In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. It is well-known that the direction generated by a conjugate gradient method may not be a descent direction of the objective function. In this paper, we take a little modification to the Fletcher-Reeves (FR) method such that the direction generated by the modified method provides a descent direction for the objective function. This property depends neither on the line search used, nor on the convexity of the objective function. Moreover, the modified method reduces to the standard FR method if line search is exact. Under mild conditions, we prove that the modified method with Armijo-type line search is globally convergent even if the objective function is nonconvex. We also present some numerical results to show the efficiency of the proposed method.

In this paper, we propose a new hybrid coefficient of conjugate gradient method (CG) for solving unconstrained optimization model.  The new coefficient is combination of part the MMSIS (Malik et.al, 2020) and PRP (Polak, Ribi&#39;ere \& Polyak, 1969) coefficients.  Under exact line search, the search direction of new method satisfies the sufficient descent condition and based on certain assumption, we establish the global convergence properties.  Using some test functions, numerical results show that the proposed method is more efficient than MMSIS method.  Besides, the new method can be used to solve problem in minimizing portfolio selection risk .

It is well known that the hybrid conjugate gradient method plays a main role for solving large-scale minimization problems. In this paper, we propose a new new hybrid DY and HS conjugate gradient method. Dai and Yuan developed a conjugate gradient method, which has good numerical performance and global convergence result under line searches such as Wolfe and strong Wolfe line search . Recently, we propose a modi…cation of the Dai–Yuan conjugate gradient algorithm, which produces a descent search direction at every iteration and converges globally provided that the line search satis…es the weak Wolfe

The Hestenes-Stiefel (HS) conjugate gradient algorithm is a useful tool of unconstrained numerical optimization, which has good numerical performance but no global convergence result under traditional line searches. This paper proposes a line search technique that guarantee the global convergence of the Hestenes-Stiefel (HS) conjugate gradient method. Numerical tests are presented to validate the different approaches.

A numerical method is proposed to solve the two-layer inviscid, incompressible and immiscible 1D shallow-water equations in a moving vessel with a rigid-lid with different boundary conditions based on the high-resolution f-wave finite volume methods due to Bale, LeVeque, Mitran and Rossmanith [7] (2002, SIAM J. Sci. Comput. 24). The method splits the jump in the fluxes and source terms including the pressure gradient at the rigid-lid into waves propagating away from each grid cell interface. For the influxefflux boundary conditions the time dependent source terms are handled via a fractional step approach. In the linear case the numerical solutions are validated by comparison with the exact analytical solutions. Numerical solutions presented for the nonlinear case include shallow-water sloshing waves due to prescribed surge motion of the vessel.

We consider the problem of the estimation of some parameters involved in a trip distribution model issued from the Transportation Planning. The estimators of the maximum likelihood of the model are the global minima of a non-convex functional. The numerical method must prevent convergence to local minima and we apply a new algorithm of global optimization involving random perturbations of the gradient method. Numerical experiments involving real data show that the method is eective to calculate.

Modulation transfer function (MTF) metrology and interpretation for digital image capture devices has usually concentrated on mid-to high-frequency information, relative to the half-sampling frequency. These regions typically quantify characteristics and operations such as sharpening, limiting resolution, and aliasing. However, a potential wealth of low-frequency, visually significant information is often masked in existing measurement results because of spatial data truncation. For print or document scanners, this influences measurements in the spatial frequency range of 0 to 2.0 cycles/mm, where the effects of veiling flare, micro flare, and integrating cavity effect (ICE) often manifest themselves. Using a form of edge-gradient analysis based on slanted edges, we present a method for measurement of these characteristics. By carefully adapting this well-established technique, these phenomena can be quantified. We also show how, in many cases, these effects can be treated as other spread-function or device-MTF components. The theory and field metrology of several devices using the adapted technique are also presented.