Optimality conditions, duality and saddle points for nondifferentiable multiobjective fractional programs

Xian-Jun Long; Nan-Jing Huang; Zhi-Bin Liu

doi:10.3934/jimo.2008.4.287

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2008, Volume 4, Issue 2: 287-298. Doi: 10.3934/jimo.2008.4.287

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Optimality conditions, duality and saddle points for nondifferentiable multiobjective fractional programs

1.
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064
2.
Department of Applied Mathematics, Southwest Petroleum University, Chengdu, Sichuan 610500

Received: December 31, 2006

Revised: July 31, 2007

Published: March 2008

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Abstract

In this paper, a class of nondifferentiable multiobjective fractional programs is studied, in which every component of the objective function contains a term involving the support function of a compact convex set. Kuhn-Tucker necessary and sufficient optimality conditions, duality and saddle point results for weakly efficient solutions of the nondifferentiable multiobjective fractional programming problems are given. The results presented in this paper improve and extend some the corresponding results in the literature.

Keywords:

Nondifferentiable multiobjective fractional programming,
Kuhn-Tucker optimality condition,
duality,
saddle point,
weakly efficient solution,
$(F,
\alpha,
\rho,
d)$-convex function.

Mathematics Subject Classification: Primary: 90C26, 90C29; Secondary: 90C46.

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