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Operations Research Transactions >

2015 , Vol. 19 >Issue 3: 151 - 160

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2015.03.018

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

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  • 1. School of Management, Qufu Normal University,  Shandong Qufu 273165, China; 2. School of Science, Shandong University of Technology, Shandong  Zibo 255049, China

Received date: 2015-06-06

  Online published: 2015-09-15

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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

Cite this article

WANG Changyu, ZHAO Wenling . Global convergence of a class smooth penalty algorithm of constrained optimization problem[J]. Operations Research Transactions, 2015 , 19(3) : 151 -160 . DOI: 10.15960/j.cnki.issn.1007-6093.2015.03.018

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