不等式约束优化问题的低阶精确罚函数的光滑化算法

对不等式约束优化问题提出了一个低阶精确罚函数的光滑化算法. 首先给出了光滑罚问题、非光滑罚问题及原问题的目标函数值之间的误差估计，进而在弱的假
设之下证明了光滑罚问题的全局最优解是原问题的近似全局最优解. 最后给出了一个基于光滑罚函数的求解原问题的算法，证明了算法的收敛性，并给出数值算例说明算法的可行性.

On the smoothing of the lower order exact penalty function for inequality constrained optimization

In this paper, we propose a method to smooth the general lower order exact penalty function for inequality constrained optimization. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth penalty problem and of the original optimization problem. It is shown that under mild assumption, an approximate global solution of the original problem can be obtained by searching a global solution of the smoothed penalty problem. We develop an algorithm for solving the original optimization problem based on the smoothed penalty function and prove the convergence of the algorithm. Some numerical examples are given to illustrate the applicability of the present smoothing method.