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A Collaborative Neurodynamic Approach to Distributed Global Optimization

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2023年第5期53卷 3141-3151页

作者： Xia, Zicong Liu, Yang Wang, Jun Zhejiang Normal Univ Coll Math & Comp Sci Jinhua 321004 Peoples R China Zhejiang Normal Univ Key Lab Intelligent Educ Technol & Applicat Zhejia Jinhua 321004 Peoples R China Zhejiang Normal Univ Coll Math & Comp Sci Jinhua 321004 Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China City Univ Hong Kong Sch Data Sci Hong Kong Peoples R China

In this article, we present a collaborative neurodynamic approach to distributed optimization with nonconvex functions. We develop a recurrent neural network (RNN) group by connecting individual projection neural networks through a communication network. We prove the convergence of the RNN group to the local optimal solutions of a given distributed optimization problem. We propose a collaborative neurodynamic optimization system with multiple RNN groups for scattered searches and a metaheuristic rule for reinitializing the neuronal states upon their local convergence. We elaborate on three numerical examples to demonstrate the efficacy of the proposed approach to distributed global optimization in the presence of nonconvexity.

关键词： Collaborative neurodynamic optimization (CNO) distributed optimization nonconvex functions recurrent neural networks (RNNs)

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A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems

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NUMERICAL ALGORITHMS 2023年第3期93卷 949-970页

作者： Wang, Xiaoliang Yuan, Gonglin Pang, Liping Zhejiang Sci Tech Univ Sch Sci Hangzhou 310018 Zhejiang Peoples R China Guangxi Univ Coll Math & Informat Sci Ctr Appl Math Guangxi Nanning 530004 Guangxi Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Liaoning Peoples R China

Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems since they have attractive practical factors such as simple computation, low memory requirement and strong global convergence property. Based on the sufficient descent property and the Dai-Liao conjugate condition, a class of new three-term descent conjugate gradient algorithms are proposed. The proposed algorithms automatically have the sufficient descent property and satisfy the conjugate condition. Under the standard Wolfe line search technique and some common conditions, the global convergence of the proposed algorithms for uniformly convex function and general nonlinear function are established. Numerical results also indicate that the proposed algorithms are more efficient and reliable than the other methods for the testing problems. At last, the proposed methods are applied to some image restoration problems.

关键词： Conjugate gradient nonconvex functions Sufficient descent property Global convergence Gradient Lipschitz continuity condition

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Solving combined heat and power economic dispatch using a mixed integer model

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JOURNAL OF CLEANER PRODUCTION 2024年 444卷

作者： Hasanabadi, Reihaneh Sharifzadeh, Hossein Hakim Sabzevari Univ Dept Elect & Comp Engn Sabzevar Iran

Combined heat and power economic dispatch (CHPED) can enhance energy efficiency compared with conventional economic dispatch (ED). From the optimization standpoint, the CHPED problem usually involves the nonlinear products of heat and power generation variables, nonconvex objective functions, and nonconvex feasible operating range. Thus, its solution method should be able to cope with the problematic nonconvex problem since finding a poor solution for the CHPED implies reducing the maximum achievable efficiency. This paper presents an effective method utilizing several mathematical transformations to cope with the nonlinear, nonconvex terms. The method transforms the nonconvex regions and nonlinear functions into convex polyhedrons and segments. Then, the method formulates the polyhedrons and segments with integer variables, logical constraints, and combinatorial restrictions. Thus, we derive a mixed integer model, which optimization software can better solve. Simulation results illustrate the effectiveness of the method presented and its advantages compared with existing CHPED solution techniques in the literature.

关键词： Combined heat and power economic dispatch Mixed-integer Piecewise linear nonconvex functions

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A conjugate gradient algorithm and its applications in image restoration

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APPLIED NUMERICAL MATHEMATICS 2020年 152卷 243-252页

作者： Cao, Junyue Wu, Jinzhao Chinese Acad Sci Chengdu Inst Comp Applicat Chengdu Peoples R China Univ Chinese Acad Sci Beijing Peoples R China Guangxi Univ Nationalities Guangxi Key Lab Hybrid Computat & IC Design Anal Nanning 530006 Peoples R China Guangxi Univ Sch Comp & Elect Informat Nanning 530004 Peoples R China

In this paper, a nonlinear conjugate gradient algorithm is presented. This given algorithm possesses the following properties: (i) the sufficient descent property is satisfied;(ii) the trust region feature holds;(iii) the global convergence is proved for nonconvex functions;(iv) the applications for image restoration problem are done to show the performance of the proposed algorithm. Notice that the properties (i) and (ii) will be obtained without other special conditions. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Conjugate gradient Impulse noise Global convergence Inexact line search nonconvex functions

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The Projection Technique for Two Open Problems of Unconstrained Optimization Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2020年第2期186卷 590-619页

作者： Yuan, Gonglin Wang, Xiaoliang Sheng, Zhou Guangxi Univ Coll Math & Informat Sci Nanning 530004 Guangxi Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Liaoning Peoples R China Nanjing Univ Aeronaut & Astronaut Dept Math Nanjing 211106 Jiangsu Peoples R China

There are two problems for nonconvex functions under the weak Wolfe-Powell line search in unconstrained optimization problems. The first one is the global convergence of the Polak-Ribiere-Polyak conjugate gradient algorithm and the second is the global convergence of the Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method. Many scholars have proven that the two problems do not converge, even under an exact line search. Two circle counterexamples were proposed to generate the nonconvergence of the Polak-Ribiere-Polyak algorithm for the nonconvex functions under the exact line search, which inspired us to define a new technique to jump out of the circle point and obtain the global convergence. Thus, a new Polak-Ribiere-Polyak algorithm is designed by the following steps. (i) Given the current point and a parabolic surface is designed;(ii) An assistant point is defined based on the current point;(iii) The assistant point is projected onto the surface to generate the next point;(iv) The presented algorithm has the global convergence for nonconvex functions with the weak Wolfe-Powell line search. A similar technique is used for the quasi-Newton method to get a new quasi-Newton algorithm and to establish its global convergence. Numerical results show that the given algorithms are more competitive than other similar algorithms. Meanwhile, the well-known hydrologic engineering application problem, called parameter estimation problem of nonlinear Muskingum model, is also done by the proposed algorithms.

关键词： Nonlinear programming PRP method BFGS method Global convergence nonconvex functions Muskingum model

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The global proof of the Polak-Ribiere-Polak algorithm under the YWL inexact line search technique

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2019年第1期2019卷 1-13页

作者： Li, Xiangrong Yang, Tianshan Wang, Xiaoliang Guangxi Univ Coll Math & Informat Sci Nanning Peoples R China Nanning Coll Vocat Technol Sch Finance & Econ Nanning Peoples R China Dalian Univ Technol Sch Math Sci Dalian Peoples R China

This paper presents a new proof method about the paper (Yuan et al. in Appl. Math. Model. 47:811-825, 2017). In the proof, the global convergence of the Polak-Ribiere-Polak algorithm is established without these two assumptions dkT dk which are needed in the above paper. This means that this paper has the same results under weaker conditions. More dimension functions for practical problems are tested to show the performance of the modified algorithm and the normal algorithm. An application of the fact engineering model is done to show the effectiveness of the given conjugate gradient algorithm.

关键词： PRP method Global convergence WWP line search nonconvex functions Muskingum model

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nonconvex Weak Sharp Minima on Riemannian Manifolds

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2019年第1期183卷 85-104页

作者： Karkhaneei, Mohammad Mahdi Mahdavi-Amiri, Nezam Sharif Univ Technol Tehran Iran

We establish some necessary conditions (of the primal and dual types) for the set of weak sharp minima of a nonconvex optimization problem on a Riemannian manifold. Here, we provide a generalization of some characterizations of weak sharp minima for convex problems on Riemannian manifold introduced by Li et al. (SIAM J Optim 21(4):1523-1560, 2011) for nonconvex problems. We use the theory of the Frechet and limiting subdifferentials on Riemannian manifold to give some necessary conditions of the dual type. We also consider a theory of contingent directional derivative and a notion of contingent cone on Riemannian manifold to give some necessary conditions of the primal type. Several definitions have been provided for the contingent cone on Riemannian manifold. We show that these definitions, under some modifications, are equivalent. We establish a lemma about the local behavior of a distance function. We use this lemma to establish some necessary conditions by expressing the Frechet subdifferential (contingent directional derivative) of a distance function on a Riemannian manifold in terms of normal cones (contingent cones). As an application, we show how one can use weak sharp minima property to model a Cheeger-type constant of a graph as an optimization problem on a Stiefel manifold.

关键词： Weak sharp minima Riemannian manifolds Distance functions nonconvex functions Generalized differentiation Graph clustering

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Local convergence of the proximal point method for a special class of nonconvex functions on Hadamard manifolds

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2010年第2期73卷 564-572页

作者： Bento, G. C. Ferreira, O. P. Oliveira, P. R. Univ Fed Goias IME BR-74001970 Goionia Go Brazil Univ Fed Rio de Janeiro COPPE Sistemas BR-21945970 Rio De Janeiro Brazil

Local convergence analysis of the proximal point method for a special class of nonconvex functions on Hadamard manifold is presented in this paper. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, it is proved that each cluster point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minimizer is obtained. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Proximal point method nonconvex functions Hadamard manifolds

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Design of Gaussian inputs for Wiener model identification

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IFAC-PapersOnLine 2015年第28期48卷 614-619页

作者： Mahata, Kaushik Schoukens, Johan De Cock, Alexander School of Electrical Engineering University of Newcastle Callaghan NSW 2308 Australia Department ELEC Vrije Universiteit Brussel Building K Pleinlaan 2 1050 Brussels Belgium

We develop a tractable algorithms for finding the optimal power spectral density of the Gaussian input excitation for identifying a Wiener model. This problem is known as a difficult problem for two reasons. Firstly, the estimation accuracy depends on the higher order joint moments of the potentially infinitely many past samples of the input signal. In addition, the covariancematrix of the parameter estimates is thought to be a highly non-convex function of the power spectral density function. In this contribution we show that under Gaussian assumption it is possible to completely parameterize the set of all admissible information matrices with only a finite number of parameters. We present a convex algorithm to solve the D-optimal design problem. This idea can be extended further to design Gaussian mixture designs. © 2015

关键词： Gaussian distribution functions Power spectral density Spectral density Convex algorithm D optimal designs Gaussian assumption Gaussian inputs Gaussian mixtures nonconvex functions Parameter estimate Tractable algorithms

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Comparative Study of the CG and HBF ODEs Used in the Global Minimization of nonconvex functions

Comparative Study of the CG and HBF ODEs Used in the Global ...

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19th International Conference on Artificial Neural Networks (ICANN 2009)

作者： Bhaya, Amit Pazos, Fernando A. Kaszkurewicz, Eugenius Univ Fed Rio de Janeiro COPPE Dept Elect Engn BR-21945970 Rio de Janeiro Brazil

ISBN: (纸本)9783642042737

This paper presents a unified control Liapunov function (CLF) approach to the design of heavy ball with friction (HBF) and conjugate gradient (CG) neural networks that aim to minimize scalar nonconvex functions that have continuous first- and second-order derivatives and a unique global minimum. This approach leads naturally to the design of second-order differential equations which are the mathematical models of the corresponding implementations as neural networks. Preliminary numerical simulations indicate that, on a small suite of benchmark test problems, a continuous version of the well known conjugate gradient algorithm, designed by the proposed CLF method, has better performance than its HBF competitor.

关键词： Control Liapunov functions nonconvex functions Global Minimization Second Order ODEs

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