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Higher order duality in multiobjective programming with cone constraints

Do Sang Kim, Hun Suk Kang, Yu Jung Lee, YouYoung Seo

Open publisher page 10 citations

Abstract

We consider the nonlinear multiobjective programming problems involving cone constraints. For this program, we construct higher order dual problems and establish weak, strong and converse duality theorems for an efficient solution by using higher order generalized invexity conditions due to Zhang (Higher order convexity and duality in multiobjective programming, in “Progress in Optimization”, Contributions from Australasia, Applied Optimization, Vol. 30, eds. A. Eberhard, R. Hill, D. Ralph and B.M. Glover, Kluwer Academic Publishers, Dordrecht, 1999, 101–116). As special cases of our duality relations, we give some known duality results.

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What this paper is about

We consider the nonlinear multiobjective programming problems involving cone constraints. For this program, we construct higher order dual problems and establish weak, strong and converse duality theorems for an efficient solution by using higher order generalized invexity conditions due to Zhang (Higher order convexity and duality in multiobjective programming, in “Progress in Optimization”, Contributions from Australasia, Applied Optimization, Vol. 30, eds. A. Eberhard, R. Hill, D. Ralph and B.M. Glover, Kluwer Academic Publishers, Dordrecht, 1999, 101–116). As special cases of our duality relations, we give some known duality results.

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Available abstract

We consider the nonlinear multiobjective programming problems involving cone constraints. For this program, we construct higher order dual problems and establish weak, strong and converse duality theorems for an efficient solution by using higher order generalized invexity conditions due to Zhang (Higher order convexity and duality in multiobjective programming, in “Progress in Optimization”, Contributions from Australasia, Applied Optimization, Vol. 30, eds. A. Eberhard, R. Hill, D. Ralph and B.M. Glover, Kluwer Academic Publishers, Dordrecht, 1999, 101–116). As special cases of our duality relations, we give some known duality results.

Key concepts: Duality (order theory), Strong duality, Mathematics, Converse, Convexity, Weak duality, Multiobjective programming, Wolfe duality

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