Abstract:

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.

Key words: The exact penalty function, The lower order exact penalty function, Smooth and exact penalty function approach, Smooth penalty algorithm, The generalized Mangasarian-Fromovitz constraint qualification