Indexed by:期刊论文

Date of Publication:2009-01-15

Journal:NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:70

Issue:2

Page Number:757-763

ISSN No.:0362-546X

Key Words:Nonconvex programming; Unbounded set; Homotopy method; Global convergence

Abstract:In the papers [G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics; Proceedings of the Second Japan-China Seminar on Numerical Mathematics, in: Lecture Notes in Numerical and Applied Analysis, vol. 14, Kinokuniya, Tokyo, 1995, pp. 9-16; G.C. Feng, Z.H. Lin, B. Yu, Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem, Nonlinear Analysis 32 (1998) 761-768; Z.H. Lin, B. Yu, G.C. Feng, A combined homotopy interior point method for convex programming problem, Applied Mathematics and Computation 84(1997) 193-211], a combined homotopy interior method was presented and global convergence results obtained for nonconvex nonlinear programming when the feasible set is bounded and satisfies the so called normal cone condition. However, for when the feasible set is not bounded, no result has so far been obtained. In this paper, a combined homotopy interior method for nonconvex programming problems oil the unbounded feasible set is considered. Under suitable additional assumptions, boundedness of the homotopy path, and hence global convergence, is proven. (C) 2008 Elsevier Ltd. All rights reserved.