约束优化问题的一类光滑罚算法的全局收敛特性（英文）

Global convergence of a class smooth penalty algorithm of constrained optimization problem

对约束优化问题给出了一类光滑罚算法.它是基于一类光滑逼近精确罚函数l_p(p∈(0,1])的光滑函数L_p而提出的.在非常弱的条件下,建立了算法的一个摄动定理,导出了算法的全局收敛性.特别地,在广义Mangasarian-Fromovitz约束规范假设下,证明了当p=1时,算法经过有限步迭代后,所有迭代点都是原问题的可行解;当p∈(0,1)时,算法经过有限迭代后,所有迭代点都是原问题可行解集的内点.

For constrained optimization problem, a class of smooth penalty algorithm is proposed. It is put forward based on Lp, a smooth function of a class of smooth exact penalty function lp （p C （0, 1））. Under the very weak condition, a perturbation theorem of the algorithm is set up. The global convergence of the algorithm is derived. In particular, under the hypothesis of generalized Mangasarian-Fromovitz constraint qualification, it is proved that when p =1, after finite iterations, all iterative points of the algorithm are feasible solutions of the original problem. When p ∈ （0, 1）, after finite iteration, all the iteration points are the interior points of feasible solution set of the original problem.