Journal of Applied Mathematics
Volume 2012 (2012), Article ID 497345, 12 pages
http://dx.doi.org/10.1155/2012/497345
Research Article

Homotopy Interior-Point Method for a General Multiobjective Programming Problem

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

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

Received 26 October 2011; Revised 10 February 2012; Accepted 12 February 2012

Academic Editor: Yongkun Li

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

We present a combined homotopy interior-point method for a general multiobjective programming problem. For solving the KKT points of the multiobjective programming problem, the homotopy equation is constructed. We prove the existence and convergence of a smooth homotopy path from almost any initial interior point to a solution of the KKT system under some basic assumptions.