A neurodynamic approach to nonlinear optimization problems with affine equality and convex inequality constraints

被引:65
|
作者
Liu, Na [1 ]
Qin, Sitian [1 ]
机构
[1] Harbin Inst Technol, Dept Math, Weihai, Peoples R China
基金
美国国家科学基金会;
关键词
Nonlinear optimization problems; Recurrent neural network; Lyapunov function; Global convergence; RECURRENT NEURAL-NETWORK; PSEUDOCONVEX OPTIMIZATION; DATA RECONCILIATION;
D O I
10.1016/j.neunet.2018.10.010
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
This paper presents a neurodynamic approach to nonlinear optimization problems with affine equality and convex inequality constraints. The proposed neural network endows with a time-varying auxiliary function, which can guarantee that the state of the neural network enters the feasible region in finite time and remains there thereafter. Moreover, the state with any initial point is shown to be convergent to the critical point set when the objective function is generally nonconvex. Especially, when the objective function is pseudoconvex (or convex), the state is proved to be globally convergent to an optimal solution of the considered optimization problem. Compared with other neural networks for related optimization problems, the proposed neural network in this paper has good convergence and does not depend on some additional assumptions, such as the assumption that the inequality feasible region is bounded, the assumption that the penalty parameter is sufficiently large and the assumption that the objective function is lower bounded over the equality feasible region. Finally, some numerical examples and an application in real-time data reconciliation are provided to display the well performance of the proposed neural network. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码:147 / 158
页数:12
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