Neural Network for Solving Constrained Convex Optimization Problems With Global Attractivity

作者：Bian Wei^*; Xue Xiaoping

来源：IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2013, 60(3): 710-723.

DOI：10.1109/TCSI.2012.2209735

• Differential inclusion
• global attractivity
• neural network
• nonsmooth convex optimization
• regularization method

In this paper, we propose a neural network modeled by a differential inclusion to solve a class of nonsmooth convex optimization problems, where the constraints are defined by a class of nonsmooth convex inequality constraints and a class of affine equality constraints. For any initial point, the solution of the proposed network is global existent, unique and uniformly bounded, which is just the "slow solution" of network. By the regularization item, without any estimation on the exact penalty parameters, the solution of proposed network is convergent to the optimal solution set of optimization problem. Moreover, when the feasible region satisfies another condition, the solution of proposed network converges to the feasible region in finite time and to the particular element in the optimal solution set with the smallest norm, which indicates that our proposed neural network is globally attractive. Some numerical examples are presented to illustrate the effectiveness of the proposed neural network for solving nonsmooth convex optimization problems.

• 出版日期2013-3
• 单位哈尔滨工业大学