等式约束优化问题的一类新的简单光滑精确罚函数

摘要

精确罚函数方法是求解优化问题的一类经典方法,传统的精确罚函数不可能既是简单的又是光滑的,这里简单的是指罚函数中不包含目标函数和约束函数的梯度信息.针对等式约束问题提出了不同与传统罚函数的一类新的简单光滑罚函数并证明了它是精确的.给出了以新的罚函数为基础的罚函数方法并用数值例子说明算法是可行的.%Exact penalty function method is one of the main approaches for solving constrained nonlinear programming problems.For the traditional exact penalty function,it is not both smooth and simple.It is simple in the sense that the gradient of the objective function and constrained functions is not involved in the penalty function.In this paper,a new class of simple and smooth penalty functions which are different from the tradition penalty functions is proposed for the equality constrained problem.It is proved that the class of exact penalty functions is exact.The algorithm based on the new smoothed penalty functions is proposed.Two numerical examples show that the algorithm is efficient.