约束优化问题的一类光滑罚算法的全局收敛特性

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\in(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; p\in(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.

Global convergence of a class smooth penalty algorithmof constrained optimization problem

For constrained optimization problem, a class of smooth penalty algorithm is proposed. It is put forward based on L_p , a smooth function of a class of smooth exact penalty function {l_p}\left( {p\in (0,1]} \right).Under the very weak condition, a perturbationtheorem 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 \in (0,1)}, after finite iteration, all the iteration points are the interior points of feasible solution set of the original problem.