求解混合约束极大极小问题的精确光滑罚函数法

A Exact and Smooth Penalty Function for Solving Mixed Constrained Min-Max Problems

提出一个新的精确光滑罚函数法求解混合约束极大极小问题,通过引入一个新变量,将带混合约束的极大极小问题转化为等价的无约束优化问题,证明在合理的假设条件下,罚问题的极小点就是原问题的极小点,数值实验表明新算法是求解带混合约束的极大极小问题的一种有效算法.

A new exact and smooth penalty function was introduced to solve min-max problem of equality and inequality constraints.Though adding a new variable,the mixed constraints min-max problem is transformed to equivalent unconstrained optimization problem.It is proved that,under certain reasonable assumptions,the minimum point of unconstrained optimization problem was equivalent to the minimum point of the original constrained one.The numerical results demonstrate that the new method is an effective approach for solving mixed constrained min-max problems.