Papers by Dr.Keyvan Amini
A new three-term spectral subgradient method for solving absolute value equation
International Journal of Computer Mathematics, Sep 30, 2022
Research Square (Research Square), Jul 28, 2022
This paper presents a new diagonal quasi-Newton method for solving unconstrained optimization pro... more This paper presents a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. The new method uses new criteria to generate the Hessian approximation to control the diagonal elements. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems show that the proposed method is superior to several certain diagonal methods.
A Globally Convergent Trust-Region Method for Large-Scale Symmetric Nonlinear Systems
Numerical Functional Analysis and Optimization, May 7, 2015
Journal of Computational and Applied Mathematics, Mar 1, 2020
In this paper, we propose a modified two-step trust-region algorithm for solving nonlinear system... more In this paper, we propose a modified two-step trust-region algorithm for solving nonlinear systems. Two-step trust-region algorithms, at every iteration, use a trust-region step and an approximate step by saving the Jacobian matrix to have fewer computations. We introduce a convex combination to modify the trust-region subproblems along with an additional criterion to verify whether the first step is accepted or not. We establish global and quadratic convergence of the algorithm under some mild assumptions. Numerical results show that the modified algorithm is efficient and promising.
Journal of Computational and Applied Mathematics, Jun 1, 2010
This paper presents a modified quasi-Newton method for structured unconstrained optimization. The... more This paper presents a modified quasi-Newton method for structured unconstrained optimization. The usual SQN equation employs only the gradients, but ignores the available function value information. Several researchers paid attention to other secant conditions to get a better approximation of the Hessian matrix of the objective function. Recently Yabe et al. (2007) [6] proposed the modified secant condition which uses both gradient and function value information in order to get a higher-order accuracy in approximating the second curvature of the objective function. In this paper, we derive a new progressive modified SQN equation, with a vector parameter which use both available gradient and function value information, that maintains most properties of the usual and modified structured quasi-Newton methods. Furthermore, local and superlinear convergence of the algorithm is obtained under some reasonable conditions.
An adaptive modified three-term conjugate gradient method with global convergence
Applied Numerical Mathematics, Aug 1, 2023
DergiPark (Istanbul University), Sep 1, 2019
It is well known that the sufficient descent condition is very important to the global convergenc... more It is well known that the sufficient descent condition is very important to the global convergence of the nonlinear conjugate gradient methods. Also, the direction generated by a conjugate gradient method may not be a descent direction. In this paper, we propose a new Armijo-type line search algorithm such that the direction generated by the PRP conjugate gradient method has the sufficient descent property and ensures the global convergence of the PRP conjugate gradient method for the unconstrained minimization of nonconvex differentiable functions. We also present some numerical results to show the efficiency of the proposed method.The results show the efficiency of the proposed method in the sense of the performance profile introduced by Dolan and Moré.
Three-steps modified Levenberg–Marquardt method with a new line search for systems of nonlinear equations
Journal of Computational and Applied Mathematics, Jul 1, 2016
Three steps modified Levenberg-Marquardt method for nonlinear equations was introduced by Yang (2... more Three steps modified Levenberg-Marquardt method for nonlinear equations was introduced by Yang (2013). This method uses the addition of the Levenberg-Marquardt (LM) step and two approximate LM steps as the trial step at every iteration. Using trust region technique, the global and biquadratic convergence of the method is proved by Yang. The main aim of this paper is to introduce a new line search strategy while investigating the convergence properties of the method with this line search technique. Since the search direction of Yang method may be not a descent direction, standard line searches cannot be used directly. In this paper we propose a new nonmonotone third order Armijo type line search technique which guarantees the global convergence of this method while we use an adaptive LM parameter. It is proved that the convergence order of the new method is biquadratic. Numerical results show the new algorithm is efficient and promising.
A Modified Levenberg-Marquardt Method with a Non-Monotone Line Search for Solving Systems of Nonlinear Equations
This paper presents a new diagonal quasi-Newton method for solving unconstrained optimization pro... more This paper presents a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. The new method uses new criteria to generate the Hessian approximation to control the diagonal elements. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems show that the proposed method is superior to several certain diagonal methods.Mathematics subject classification 90C30 . 65K05
Global convergence of a modified spectral three-term CG algorithm for nonconvex unconstrained optimization problems
Journal of Computational and Applied Mathematics
DergiPark (Istanbul University), Sep 1, 2019
It is well known that the sufficient descent condition is very important to the global convergenc... more It is well known that the sufficient descent condition is very important to the global convergence of the nonlinear conjugate gradient methods. Also, the direction generated by a conjugate gradient method may not be a descent direction. In this paper, we propose a new Armijo-type line search algorithm such that the direction generated by the PRP conjugate gradient method has the sufficient descent property and ensures the global convergence of the PRP conjugate gradient method for the unconstrained minimization of nonconvex differentiable functions. We also present some numerical results to show the efficiency of the proposed method.The results show the efficiency of the proposed method in the sense of the performance profile introduced by Dolan and Moré.
A spectral conjugate gradient projection algorithm to solve the large-scale system of monotone nonlinear equations with application to compressed sensing
International Journal of Computer Mathematics, 2022
A New Strategy for Choosing the Radius Adjusting Parameters in Trust Region Methods
arXiv: Optimization and Control, 2019
In this paper, we propose a new conjugate gradient-like algorithm. The step directions generated ... more In this paper, we propose a new conjugate gradient-like algorithm. The step directions generated by the new algorithm satisfy a sufficient descent condition independent of the line search. The global convergence of the new algorithm, with the Armijo backtracking line search, is proved. Numerical experiments indicate the efficiency and robustness of the new algorithm in solving a collection of unconstrained optimization problems from CUTEst package.
Three-steps modified Levenberg–Marquardt method with a new line search for systems of nonlinear equations
Journal of Computational and Applied Mathematics, 2016
Three steps modified Levenberg-Marquardt method for nonlinear equations was introduced by Yang (2... more Three steps modified Levenberg-Marquardt method for nonlinear equations was introduced by Yang (2013). This method uses the addition of the Levenberg-Marquardt (LM) step and two approximate LM steps as the trial step at every iteration. Using trust region technique, the global and biquadratic convergence of the method is proved by Yang. The main aim of this paper is to introduce a new line search strategy while investigating the convergence properties of the method with this line search technique. Since the search direction of Yang method may be not a descent direction, standard line searches cannot be used directly. In this paper we propose a new nonmonotone third order Armijo type line search technique which guarantees the global convergence of this method while we use an adaptive LM parameter. It is proved that the convergence order of the new method is biquadratic. Numerical results show the new algorithm is efficient and promising.
A new PRP-Armijo conjugate gradient methods with global convergence
The PRP conjugate gradient method is generally not a descent method when Armijo line search is us... more The PRP conjugate gradient method is generally not a descent method when Armijo line search is used. Since, the sufficient descent condition is very important to the global convergence of the nonlinear conjugate gradient methods, so, in this paper, we propose a new Armijo-type line search algorithm such that the direction generated by the PRP conjugate gradient method has sufficient descent property and ensures the global convergence of the PRP conjugate gradient method for the unconstrained minimization of nonconvex differentiable functions. We also present some numerical results to show the efficiency of the proposed method
Bulletin of the Australian Mathematical Society, 2004
ABS mthods are direct iteration methods for solving linear systems where the i-th iterate satisfi... more ABS mthods are direct iteration methods for solving linear systems where the i-th iterate satisfies the first i equations, and therefore a system on m equations is solved in at most m ABS steps. In this paper, using a new rank two update of the Abaffian matrix, we introduce a class of ABS-type methods for solving full row rank linear equations, where the i-th iterate solves the first 2i equations. So, termination is achieved in at most ⌊(m + 1)/2⌋ steps. We also show how to decrease the dimension of the Abaffian matrix by choosing appropriate parameters.
Applications of Mathematics
In this paper, we propose a new and efficient nonmonotone adaptive trust region algorithm to solv... more In this paper, we propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for adjusting the trust region radius that avoids undesirable directions and it exploits a new strategy to prevent sudden increments of objective function values in nonmonotone trust region techniques. Global convergence of this algorithm is investigated under some mild conditions. Numerical experiments demonstrate the efficiency and robustness of the proposed algorithm in solving a collection of unconstrained optimization problems from the CUTEst package.
An efficient nonmonotone adaptive trust region method for unconstrained optimization
arXiv: Optimization and Control, 2019
In this paper, we propose a new and efficient nonmonotone adaptive trust region algorithm to solv... more In this paper, we propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for adjusting the trust region radius that avoids undesirable directions; and it exploits a strategy to prevent sudden increments of objective function values in nonmonotone trust region techniques. Global convergence of this algorithm is investigated under mild conditions. Numerical experiments demonstrate the efficiency and robustness of the proposed algorithm in solving a collection of unconstrained optimization problems from CUTEst package.
Uploads
Papers by Dr.Keyvan Amini