Symmetric Duality in Multi – Objective Programming

Dr. Riddhi Garg

doi:https://doi.org/10.14445/22315373/IJMTT-V29P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 29 | Number 1 | Year 2016 | Article Id. IJMTT-V29P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V29P507

Symmetric Duality in Multi – Objective Programming

Dr. Riddhi Garg

Citation :

Dr. Riddhi Garg, "Symmetric Duality in Multi – Objective Programming," International Journal of Mathematics Trends and Technology (IJMTT), vol. 29, no. 1, pp. 39-44, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V29P507

Abstract

Dorn introduced symmetric duality in nonlinear programming by defining a program and it’s dual to be symmetric if the dual of the dual is the original problem. In the past, the symmetric duality has been studied extensively in the literature by Dantzig and Mond and Weir. Recently, Weit and Mond studied symmetric duality in the context of multi-objective programming by introducing a multi-objective analogue of the primal-dual pair presented in Mond. Although the multi-objective primal dual pair constructed in subsumes the single objective symmetric duality as a special case, the construction of seems to be somewhat restricted because the same parameter   Rp (vector multiplier corresponding to various objectives) is present in both primal and dual. Further, the proof of the main duality result assumes this  to be fixed in the dual problem. The main aim of this paper is to present a pair of multi-objective programming problem (P) and Duality (D) with  as variable in both programs and to establish symmetric duality by associating a vector-valued infinite game to this pair. Although this construction seems to be more natural than that of [13] as it does not require  to be fixed in the dual problem, it lacks the weak duality theorem as illustrated in Section3. However the case of single objective symmetric duality [7] is fully subsumed here as well, because (P) and (D) then reduce to primal – dual pair of Dantzig.

Keywords

n-dimensional Euclidean space, Vectorvalued infinite game, multi-objective programming, Symmetric duality.

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