存零约束优化问题的目标罚函数法

Objective Penalty Function Method for Mathematical Program with Switching Constraints

存零约束优化问题是一类特殊的约束优化问题。若x¯是该问题的最优解,由于存零约束,导致通常的约束规范在x¯处不成立,因此有些算法不能直接应用于求解存零约束优化问题。本文在求解传统非线性规划的目标罚函数方法的基础上,提出了一种求解存零约束优化问题的目标罚函数方法,在一定的条件下证明了目标罚函数的局部最优解是原问题的局部最优解,以及目标罚函数算法产生的迭代点列的极限点是原问题的弱稳定点。数值算例表明,本文所提出的目标罚函数方法是有效的。

The mathematical program with switching constraints is a special type of constrained optimization problem. Ifx¯is the optimal solution of the problem, due to the switching constraints, the usual constraint specification does not hold atx¯, so some algorithms cannot be directly applied to solve the mathematical program with switching constraints. On the basis of solving the objective penalty function method for traditional nonlinear programming, this article proposes an objective penalty function method for solving mathematical program with switching constraints. Under certain conditions, it is proved that the local optimal solution of the objective penalty function is the local optimal solution of the original problem, and the limit point of the iterative point sequence generated by the objective penalty function algorithm is the weakly stationary point of the original problem. Numerical examples show that the objective penalty function method proposed in this paper is effective.