Indexed by:期刊论文

Date of Publication:2012-01-01

Journal:PACIFIC JOURNAL OF OPTIMIZATION

Included Journals:SCIE、Scopus

Volume:8

Issue:1

Page Number:89-101

ISSN No.:1348-9151

Key Words:nonconvex programming; interior point method; infeasible interior point method; homotopy method; global convergence

Abstract:In this paper, a new homotopy method is proposed for solving nonconvex programming problems with both equality and inequality constraints. Existence and global convergence of the homotopy path with probability one to a solution of the KKT system are proven under a normal cone condition, which concerns only with the inequality constraints, as well as a stronger positive linear independence assumption. It requires only an interior point and not necessarily feasible point as the starting point, so it is more practical than the combined homotopy interior point method, which needs a feasible interior starting point. Simple numerical examples are given to show the feasibility and efficiency of the proposed method.