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Mathematical Problems in Engineering
Volume 2014, Article ID 835819, 10 pages
http://dx.doi.org/10.1155/2014/835819
Research Article

A Noninterior Path following Algorithm for Solving a Class of Multiobjective Programming Problems

1College of Mathematics, Luoyang Normal University, Luoyang 471022, China
2Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China
3Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China
4National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin 150080, China

Received 10 January 2014; Revised 20 July 2014; Accepted 28 July 2014; Published 13 August 2014

Academic Editor: Gerhard-Wilhelm Weber

Copyright © 2014 Menglong Su 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

Multiobjective programming problems have been widely applied to various engineering areas which include optimal design of an automotive engine, economics, and military strategies. In this paper, we propose a noninterior path following algorithm to solve a class of multiobjective programming problems. Under suitable conditions, a smooth path will be proven to exist. This can give a constructive proof of the existence of solutions and lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.