A recurrent neural network for solving a class of general variational inequalities

被引：68

作者：

Hu, Xiaolin ^{[1
]}

Wang, Jun ^{[1
]}

机构：

[1] Chinese Univ Hong Kong, Dept Automat & Comp Aided Engn, Shatin, Peoples R China

来源：

IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS | 2007年 / 37卷 / 03期

关键词：

general projection neural network (GPNN); general variational inequalities (GVIs); global asymptotic stability; global exponential stability; recurrent neural network; FUNCTIONAL-DIFFERENTIAL EQUATIONS; GLOBAL EXPONENTIAL STABILITY; PROJECTED DYNAMICAL-SYSTEMS; RATIO LIMIT THEOREMS; TIME-VARYING DELAYS; OPTIMIZATION PROBLEMS; CONSTRAINED OPTIMIZATION; DESCENT METHODS; CONVERGENCE;

D O I：

10.1109/TSMCB.2006.886166

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper presents a recurrent neural-network model for solving a special class of general variational inequalities (GVIs), which includes classical VIs as special cases. It is proved that the proposed neural network (NN) for solving this class of GVIs can be globally convergent, globally asymptotically stable, and globally exponentially stable under different conditions. The proposed NN can be viewed as a modified version of the general projection NN existing in the literature. Several numerical examples are provided to demonstrate the effectiveness and performance of the proposed NN.

引用

页码：528 / 539

页数：12

共 27 条

[1] EQUIVALENT DIFFERENTIABLE OPTIMIZATION PROBLEMS AND DESCENT METHODS FOR ASYMMETRIC VARIATIONAL INEQUALITY PROBLEMS [J].

FUKUSHIMA, M .

MATHEMATICAL PROGRAMMING, 1992, 53 (01) :99-110

[2] A novel neural network for variational inequalities with linear and nonlinear constraints [J].

Gao, XB ;

Liao, LZ ;

Qi, LQ .

IEEE TRANSACTIONS ON NEURAL NETWORKS, 2005, 16 (06) :1305-1317

[3]

Gao XB, 2001, CHINESE J ELECTRON, V10, P471

[4] GLOBAL RATIO LIMIT THEOREMS FOR SOME NONLINEAR FUNCTIONAL-DIFFERENTIAL EQUATIONS .I. [J].

GROSSBERG, S .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 74 (01) :95-+

[5]

GROSSBERG S, 1968, B AM MATH SOC, V74, P100, DOI 10.1090/S0002-9904-1968-11892-0

[6] NONLINEAR DIFFERENCE-DIFFERENTIAL EQUATIONS IN PREDICTION AND LEARNING THEORY [J].

GROSSBERG, S .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1967, 58 (04) :1329-+

[7] FINITE-DIMENSIONAL VARIATIONAL INEQUALITY AND NONLINEAR COMPLEMENTARITY-PROBLEMS - A SURVEY OF THEORY, ALGORITHMS AND APPLICATIONS [J].

HARKER, PT ;

PANG, JS .

MATHEMATICAL PROGRAMMING, 1990, 48 (02) :161-220

[8] A neural-network model for monotone linear asymmetric variational inequalities [J].

He, BS ;

Yang, H .

IEEE TRANSACTIONS ON NEURAL NETWORKS, 2000, 11 (01) :3-16

[9] NEURONS WITH GRADED RESPONSE HAVE COLLECTIVE COMPUTATIONAL PROPERTIES LIKE THOSE OF 2-STATE NEURONS [J].

HOPFIELD, JJ .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-BIOLOGICAL SCIENCES, 1984, 81 (10) :3088-3092

[10] Solving pseudomonotone variational inequalities and pseudoconvex optimization problems using the projection neural network [J].

Hu, Xiaolin ;

Wang, Jun .

IEEE TRANSACTIONS ON NEURAL NETWORKS, 2006, 17 (06) :1487-1499

← 1 2 3 →