American Institute of Mathematical Sciences

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April  2008, 4(2): 287-298. doi: 10.3934/jimo.2008.4.287

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

Xian-Jun Long 1, , Nan-Jing Huang 1, and  Zhi-Bin Liu 2,

1. 

Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China, China
2. 

Department of Applied Mathematics, Southwest Petroleum University, Chengdu, Sichuan 610500, China

Received  January 2007 Revised  August 2007 Published  April 2008

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, d)$-convex function., saddle point, \rho, \alpha, $(F, Kuhn-Tucker optimality condition, weakly efficient solution, duality.
Mathematics Subject Classification: Primary: 90C26, 90C29; Secondary: 90C4.
Citation: Xian-Jun Long, Nan-Jing Huang, Zhi-Bin Liu. Optimality conditions, duality and saddle points for nondifferentiable multiobjective fractional programs. Journal of Industrial & Management Optimization, 2008, 4 (2) : 287-298. doi: 10.3934/jimo.2008.4.287
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