Abstract and Applied Analysis
Volume 2012 (2012), Article ID 591612, 12 pages
http://dx.doi.org/10.1155/2012/591612
Research Article

Homotopy Method for a General Multiobjective Programming Problem under Generalized Quasinormal Cone Condition

X. Zhao,1,2 S. G. Zhang,2 Y. T. Yang,1 and Q. H. Liu3

1Department of Mathematics, Beihua University, Jilin 132013, China
2Department of Mathematics, Jilin University, Changchun 130001, China
3Institute of Applied Mathematics, Changchun University of Technology, Changchun 130012, China

Received 14 February 2012; Accepted 24 July 2012

Academic Editor: Irena Rachůnková

Copyright © 2012 X. Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A combined interior point homotopy continuation method is proposed for solving general multiobjective programming problem. We prove the existence and convergence of a smooth homotopy path from almost any interior initial interior point to a solution of the KKT system under some basic assumptions.