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Proximal Methods with Bregman Distances to Solve VIP on Hadamard Manifolds with Null Sectional Curvature

Journal of the Operations Research Society of China 2021年第3期9卷 499-523页

作者： Erik Alex Papa Quiroz Paulo Roberto Oliveira Universidad Nacional Mayor de San Marcos Universidad Privada del NorteLimaPeru PESC-COPPE Federal University of Rio de JaneiroRio de Janeiro CEP 21941-972Brazil

We present an extension of the proximal point method with Bregman distances to solve variational inequality problems(VIP)on Hadamard manifolds with null sectional *** some natural assumptions,as for example,the existence of solutions of the VIP and the monotonicity of the multivalued vector field,we prove that the sequence of the iterates given by the method converges to a solution of the ***,this convergence is linear or superlinear with respect to the Bregman distance.

关键词： Proximal point methods Hadamard manifolds Bregman distances variational inequality problems Monotone vector field

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New cooperative projection neural network for nonlinearly constrained variational inequality

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Science in China(Series F) 2009年第10期52卷 1766-1777页

作者： XIA YouSheng College of Mathematics and Computer Science Fuzhou University Fuzhou 350108 China

This paper proposes a new cooperative projection neural network （CPNN）, which combines automatically three individual neural network models with a common projection term. As a special case, the proposed CPNN can include three recent recurrent neural networks for solving monotone variational inequality problems with limit or linear constraints, respectively. Under the monotonicity condition of the corresponding Lagrangian mapping, the proposed CPNN is theoretically guaranteed to solve monotone variational inequality problems and a class of nonmonotone variational inequality problems with linear and nonlinear constraints. Unlike the extended projection neural network, the proposed CPNN has no limitation on the initial point for global convergence. Compared with other related cooperative neural networks and numerical optimization algorithms, the proposed CPNN has a low computational complexity and requires weak convergence conditions. An application in real-time grasping force optimization and examples demonstrate good performance of the proposed CPNN.

关键词： variational inequality problems general constraints cooperative recurrent neural network complexity global convergence conditions

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The Developments of Proximal Point Algorithms

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Journal of the Operations Research Society of China 2022年第2期10卷 197-239页

作者： Xing-Ju Cai Ke Guo Fan Jiang Kai Wang Zhong-Ming Wu De-Ren Han Jiangsu Key Lab for NSLSCS School of Mathematical SciencesNanjing Normal UniversityNanjing 210023JiangsuChina School of Mathematics and Information China West Normal UniversityNanchong 637002SichuanChina 不详

The problem of finding a zero point of a maximal monotone operator plays a central role in modeling many application problems arising from various fields,and the proximal point algorithm(PPA)is among the fundamental algorithms for solving the zero-finding *** not only provides a very general framework of analyzing convergence and rate of convergence of many algorithms,but also can be very efficient in solving some structured *** this paper,we give a survey on the developments of PPA and its variants,including the recent results with linear proximal term,with the nonlinear proximal term,as well as the inexact forms with various approximate criteria.

关键词： Zero-finding problems Proximal point algorithms variational inequality problems Optimization Bregman distance Approximate criteria

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New cooperative projection neural network for nonlinearly constrained variational inequality

New cooperative projection neural network for nonlinearly co...

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2009年中国智能自动化会议

作者： XIA YouSheng College of Mathematics and Computer Science,Fuzhou University,Fuzhou 350108,China

This paper proposes a new cooperative projection neural network(CPNN),which combines automatically three individual neural network models with a common projection *** a special case,the proposed CPNN can include three recent recurrent neural networks for solving monotone variational inequality problems with limit or linear constraints,*** the monotonicity condition of the corresponding Lagrangian mapping,the proposed CPNN is theoretically guaranteed to solve monotone variational inequality problems and a class of nonmonotone variational inequality problems with linear and nonlinear *** the extended projection neural network,the proposed CPNN has no limitation on the initial point for global *** with other related cooperative neural networks and numerical optimization algorithms,the proposed CPNN has a low computational complexity and requires weak convergence *** application in real-time grasping force optimization and examples demonstrate good performance of the proposed CPNN.

关键词： variational inequality problems general constraints cooperative recurrent neural network complexity global convergence conditions

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