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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 573408, 6 pages
http://dx.doi.org/10.1155/2013/573408
Research Article

Lagrangian Duality for Multiobjective Programming Problems in Lexicographic Order

1School of Information Engineering, Chongqing City Management Vocational College, Chongqing 401331, China
2Chongqing Water Resources and Electric Engineering College, Chongqing 402160, China

Received 27 April 2013; Revised 19 September 2013; Accepted 22 September 2013

Academic Editor: Shawn X. Wang

Copyright © 2013 X. F. Hu and L. N. Wang. 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

This paper deals with a constraint multiobjective programming problem and its dual problem in the lexicographic order. We establish some duality theorems and present several existence results of a Lagrange multiplier and a lexicographic saddle point theorem. Meanwhile, we study the relations between the lexicographic saddle point and the lexicographic solution to a multiobjective programming problem.