Papers by Predrag Stanimirovic
Facta Universitatis, Series: Mathematics and Informatics, Jan 10, 2018
A novel kind of a hybrid recursive neural implicit dynamics for real-time matrix inversion has be... more A novel kind of a hybrid recursive neural implicit dynamics for real-time matrix inversion has been recently proposed and investigated. Our goal is to compare the hybrid recursive neural implicit dynamics on the one hand, and conventional explicit neural dynamics on the other hand. Simulation results show that the hybrid model can coincide better with systems in practice and has higher abilities in representing dynamic systems. More importantly, hybrid model can achieve superior convergence performance in comparison with the existing dynamic systems, specifically recently-proposed Zhang dynamics. This paper presents the Simulink model of a hybrid recursive neural implicit dynamics and gives a simulation and comparison to the existing Zhang dynamics for real-time matrix inversion. Simulation results confirm a superior convergence of the hybrid model compared to Zhang model.
Operations Research Forum, Mar 29, 2021
The Markowitz mean-variance portfolio selection is widely acclaimed as a very important investmen... more The Markowitz mean-variance portfolio selection is widely acclaimed as a very important investment strategy. A popular option to solve the static mean-variance portfolio selection (MVPS) problem is based on the use of quadratic programming (QP) methods. On the other hand, the static portfolio selection under transaction costs (PSTC) problem is usually approached with nonlinear programming (NLP) methods. In this article, we define and study the time-varying meanvariance portfolio selection under transaction costs and cardinality constraint (TV-MVPSTC-CC) problem as a time-varying nonlinear programming (TVNLP) problem. The TV-MVPSTC-CC also comprises the properties of a moving average. These properties make the TV-MVPSTC-CC an even greater analysis tool suitable to evaluate investments and identify trading opportunities across a continuous-time period. Using the Beetle Antennae Search (BAS) algorithm, we also provide an online solution to the static NLP problem. To the best of our knowledge, this is an innovative approach that incorporates modern meta-heuristic optimization techniques to provide an online, thus more realistic, solution to the TV-MVPSTC-CC problem. In this way, we present an online solution to a timevarying financial problem while eliminating the restrictions of static methods. Our approach is also verified by numerical experiments and computer simulations as an excellent alternative to traditional approaches.
CAAI Transactions on Intelligence Technology, Mar 15, 2021
A special recurrent neural network (RNN), that is the zeroing neural network (ZNN), is adopted to... more A special recurrent neural network (RNN), that is the zeroing neural network (ZNN), is adopted to find solutions to time-varying quadratic programming (TVQP) problems with equality and inequality constraints. However, there are some weaknesses in activation functions of traditional ZNN models, including convex restriction and redundant formulation. With the aid of different activation functions, modified ZNN models are obtained to overcome the drawbacks for solving TVQP problems. Theoretical and experimental research indicate that the proposed models are better and more effective at solving such TVQP problems. As a kind of common and basic optimisation problem [1], the quadratic programming (QP) problem is extensively available in various scientific and technological fields [2,3], such as pattern recognition [4], signal processing and robotics . In order to deal with such problems, numerous target approaches are put forward, most of which require numerical calculations. However, the complexity and costs of numerically solving QP problems are rather high, which is proportional to the cube of the dimension of its associated Hessian matrix . Therefore, when dealing with relatively complex problems, most Xiaoyan Zhang and Liangming Chen are co-first authors and they are graduate students.
An efficient zeroing neural network for solving time-varying nonlinear equations
Neural Computing and Applications, May 12, 2023
Mathematics, Jun 6, 2022
This research introduces three novel zeroing neural network (ZNN) models for addressing the time-... more This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang-Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising from the equation involved in the TV-YBLME. Moreover, two ZNN models are proposed using basic properties of the YBLME, such as the splitting of the YBLME and sufficient conditions for a matrix to solve the YBLME. The Tikhonov regularization principle enables addressing the TV-YBLME with an arbitrary input real TV matrix. Numerical experiments, including nonsingular and singular TV input matrices, show that the suggested models deal effectively with the TV-YBLME.
Applied and Computational Mechanics, Dec 1, 2020
In this article, a simple and new algorithm is proposed, namely the modified variational iteratio... more In this article, a simple and new algorithm is proposed, namely the modified variational iteration algorithm-I (mVIA-I), for obtaining numerical solutions to different types of fifth-order Korteweg de-Vries (KdV) equations. In order to verify the precision, accuracy and stability of the mVIA-I method, generated numerical results are compared with the Laplace decomposition method, Adomian decomposition method, Homotopy perturbation transform method and the modified Adomian decomposition method. Comparison with the mentioned methods reveals that the mVIA-I is computationally attractive, exceptionally productive and achieves better accuracy than the others.
A note on the stability of apth order iteration for finding generalized inverses
Applied Mathematics Letters, Feb 1, 2014
ABSTRACT
Neural dynamics for improving optimiser in deep learning with noise considered
CAAI Transactions on Intelligence Technology, Jul 16, 2023
As deep learning evolves, neural network structures become increasingly sophisticated, bringing a... more As deep learning evolves, neural network structures become increasingly sophisticated, bringing a series of new optimisation challenges. For example, deep neural networks (DNNs) are vulnerable to a variety of attacks. Training neural networks under privacy constraints is a method to alleviate privacy leakage, and one way to do this is to add noise to the gradient. However, the existing optimisers suffer from weak convergence in the presence of increased noise during training, which leads to a low robustness of the optimiser. To stabilise and improve the convergence of DNNs, the authors propose a neural dynamics (ND) optimiser, which is inspired by the zeroing neural dynamics originated from zeroing neural networks. The authors first analyse the relationship between DNNs and control systems. Then, the authors construct the ND optimiser to update network parameters. Moreover, the proposed ND optimiser alleviates the non‐convergence problem that may be suffered by adding noise to the gradient from different scenarios. Furthermore, experiments are conducted on different neural network structures, including ResNet18, ResNet34, Inception‐v3, MobileNet, and long and short‐term memory network. Comparative results using CIFAR, YouTube Faces, and R8 datasets demonstrate that the ND optimiser improves the accuracy and stability of DNNs under noise‐free and noise‐polluted conditions. The source code is publicly available at https://github.com/LongJin‐lab/ND.
Properties and computation of continuous-time solutions to linear systems
Applied Mathematics and Computation, Sep 1, 2021
arXiv (Cornell University), Jul 8, 2018
The paper proposes a novel nature-inspired technique of optimization. It mimics the perching natu... more The paper proposes a novel nature-inspired technique of optimization. It mimics the perching nature of eagles and uses mathematical formulations to introduce a new addition to metaheuristic algorithms. The nature of the proposed algorithm is based on exploration and exploitation. The proposed algorithm is developed into two versions with some modifications. In the first phase, it undergoes a rigorous analysis to find out their performance. In the second phase it is benchmarked using ten functions of two categories; uni-modal functions and multi-modal functions. In the third phase, we conducted a detailed analysis of the algorithm by exploiting its controlling units or variables. In the fourth and last phase, we consider real world optimization problems with constraints. Both versions of the algorithm show an appreciable performance, but analysis puts more weight to the modified version. The competitive analysis shows that the proposed algorithm outperforms the other tested metaheuristic algorithms. The proposed method has better robustness and computational efficiency.
Unique non-negative definite solution of the time-varying algebraic Riccati equations with applications to stabilization of LTV systems
Mathematics and Computers in Simulation, Dec 1, 2022
A higher-order zeroing neural network for pseudoinversion of an arbitrary time-varying matrix with applications to mobile object localization
Information Sciences, Jul 1, 2022
Simulation of Varying Parameter Recurrent Neural Network with application to matrix inversion
Mathematics and Computers in Simulation, Jul 1, 2021
Symmetry
A polygon with n nodes can be divided into two subpolygons by an internal diagonal through node n... more A polygon with n nodes can be divided into two subpolygons by an internal diagonal through node n. Splitting the polygon along diagonal δi,n and diagonal δn−i,n, i∈{2,…,⌊n/2⌋} results in mirror images. Obviously, there are ⌊n/2⌋−1 pairs of these reflectively symmetrical images. The influence of the observed symmetry on polygon triangulation is studied. The central result of this research is the construction of an efficient algorithm used for generating convex polygon triangulations in minimal time and without generating repeat triangulations. The proposed algorithm uses the diagonal values of the Catalan triangle to avoid duplicate triangulations with negligible computational costs and provides significant speedups compared to known methods.
We provide existence criteria and characterizations for outer inverses in a semigroup belonging t... more We provide existence criteria and characterizations for outer inverses in a semigroup belonging to the prescribed Green’s ℛ-, ℒ- and ℋ-classes. These results generalize the well-known problem of finding outer inverses of a matrix over a field with the prescribed range or/and null space.We show that Mary’s inverse along an element, Drazin’s (b, c)-inverse, and Bott-Duffin (e,f)-inverse of a given element are just three different ways of representing the same notion – the outer inverse of this element belonging to the prescribed Green’s ℋ-class. Hence, outer inverses belonging to the prescribed Green’s ℛ- and ℒ-classes represent extensions of (b,c)-inverses and inverses along an element. We provide an overview of other such extensions that have emerged recently and compare them with the extensions introduced in this paper. Mathematics Subject Classification (2010). 20M99, 15A09, 15A24.
IEEE Transactions on Systems, Man, and Cybernetics: Systems
Facta Universitatis, Series: Mathematics and Informatics, 2021
A method of encryption of the 3D plane in Geographic Information Systems (GIS) is presented. The ... more A method of encryption of the 3D plane in Geographic Information Systems (GIS) is presented. The method is derived using Voronoi-Delaunay triangulation and properties of Catalan numbers. The Voronoi-Delaunay incremental algorithm is presented as one of the most commonly used triangulation techniques for random point selection. In accordance with the multiple applications of Catalan numbers in solving combinatorial problems and their "bit-balanced" characteristic, the process of encrypting and decrypting the coordinates of points using the Lattice Path method (walk on the integer lattice) or LIFO model is given. The triangulation of the plane started using decimal coordinates of a set of given planar points. Afterward, the resulting decimal values of the coordinates are converted to corresponding binary records and the encryption process starts by a random selection of the Catalan key according to the LIFO model. These binary coordinates are again converted into their origi...
Mathematics, 2021
This paper presents a new method of steganography based on a combination of Catalan objects and V... more This paper presents a new method of steganography based on a combination of Catalan objects and Voronoi–Delaunay triangulation. Two segments are described within the proposed method. The first segment describes the process of embedding data and generating a complex stego key. The second segment explains the extraction of a hidden message. The main goal of this paper is to transfer a message via the Internet (or some other medium) using an image so that the image remains absolutely unchanged. In this way, we prevented the potential attacker from noticing some secret message hidden in that picture. Additionally, the complex stego key consists of three completely different parts (the image, the encrypted Delaunay triangulation, and the array Rk in Base64 code), which are very difficult to relate with each other. Finally, a few security analyses of the proposed method are conducted, as well as the corresponding steganalysis.
Neural Processing Letters, 2020
A novel finite-time convergent zeroing neural network (ZNN) based on varying gain parameter for s... more A novel finite-time convergent zeroing neural network (ZNN) based on varying gain parameter for solving time-varying (TV) problems is presented. The model is based on the improvement and generalization of the finite-time ZNN (FTZNN) dynamics by means of the varying-parameter ZNN (VPZNN) dynamics, and termed as VPFTZNN. More precisely, the proposed model replaces fixed and large values of the scaling parameter by an appropriate time-dependent gain parameter, which leads to a faster and bounded convergence of the error function in comparison to previous ZNN methods. The convergence properties of the proposed VPFTZNN dynamical evolution in its generic form is verified. Particularly, VPFTZNN for solving linear matrix equations and for computing generalized inverses are investigated theoretically and numerically. Moreover, the proposed design is applicable in solving the TV matrix inversion problem, solving the Lyapunov and Sylvester equation as well as in approximating the matrix square root. Theoretical analysis as well as simulation results validate the effectiveness of the introduced dynamical evolution. The main advantages of the proposed VPFTZNN dynamics are their generality and faster finite-time convergence with respect to FTZNN models.
Symmetry, 2020
Neutrosophic sets have been recognized as an effective approach in solving complex decision-makin... more Neutrosophic sets have been recognized as an effective approach in solving complex decision-making (DM) problems, mainly when such problems are related to uncertainties, as published in numerous articles thus far. The use of the three membership functions that can be used to express accuracy, inaccuracy, and indeterminacy during the evaluation of alternatives in multiple-criteria DM can be said to be a significant advantage of these sets. By utilizing these membership functions, neutrosophic sets provide an efficient and flexible approach to the evaluation of alternatives, even if DM problems are related to uncertainty and predictions. On the other hand, the TOPSIS method is a prominent multiple-criteria decision-making method used so far to solve numerous decision-making problems, and many extensions of the TOPSIS method are proposed to enable the use of different types of fuzzy as well as neutrosophic sets. Therefore, a novel extension of the TOPSIS method adapted for the use of s...
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Papers by Predrag Stanimirovic