存零约束优化问题的部分罚函数方法

Partial Penalty Function Method for Switching Constraints Optimization Problem

存零约束优化问题是近年提出的一类新的优化问题,因存零约束的存在,使得常用的约束规范不满足,以至于现有算法的收敛性结果大多不能直接应用于该问题.文章将难处理的存零约束放于目标函数,提出了部分罚函数方法.并证明在存零约束的线性独立约束规范下,罚问题的稳定点序列的聚点为原问题的弱稳定点.同时存在罚问题的局部最优解序列收敛于原问题的任意严格局部最优解.数值结果表明该方法是可行的.

In this paper,the switching-constrained optimization problem is a new optimization problem proposed in recent years.Due to the existence of switchingconstrained,the commonly used constraint qualification is not satisfied,thus,most of the convergence results of existing algorithms cannot be directly applied to this problem.In this paper,we put the difficult switching constraint on the objective function and propose a partial penalty function method.It is proved that under the linear independent constraint qualification with switching constraint,the convergence of the sequence of stable points of the penalty problem is the weak stationary point of the original problem.At the same time,for any strictly local optimal solution of the original problem,there exists a local optimal solution sequence of the penalty problem which converges to it.Finally,numerical results show that the penalty function method is feasible.