A new optimization method based on restructuring penalty function for solving constrained minimization problems

Abstract

In this paper, a new optimization method is presented for solving the constrained minimization problems under a weak Mangasarian-Fromovit's regularity condition, Generally, there are two methods for getting all points satisfying the Kuhn-Tucker conditions. The first one is to use different initial points for a given penalty function to find the attraction region of each optimization solution. Another is to use different penalty functions to find the attraction regions of each Kuhn-Tucker point in turn to get the corresponding points satisfying the Kuhn-Tucker conditions. In this paper, a hybrid convergence algorithm based on the two methods is given for solving constrained minimization problems in which a solution of new penalty function based on the obtained Kuhn-Tucker points converges to a new Kuhn-Tucker point if it exists, thus new Kuhn-Tucker point is got continuously by different penalty function until all Kuhn-Tucker points are got. Numerical examples are provided to demonstrate its effectiveness and applicability.