The Open Operational Research Journal

2012, 6 : 1-8
Published online 2012 June 28. DOI: 10.2174/1874243201206010001
Publisher ID: TOORJ-6-1

On Multiobjective Duality For Variational Problems

I. Husain , Bilal Ahmad and Z. Jabeen
Department of Mathematics, Jaypee University of Engineering and Technology, Guna, MP, India.

ABSTRACT

In this paper two types of duals are considered for a class of variational problems involving higher order derivatives. The duality results are derived without any use of optimality conditions. One set of results is based on Mond- Weir type dual that has the same objective functional as the primal problem but different constraints. The second set of results is based on a dual of an auxiliary primal with single objective function. Under various convexity and generalized convexity assumptions, duality relationships between primal and its various duals are established. Problems with natural boundary values are considered and the analogs of our results in nonlinear programming are also indicated.

Keywords:

Variational Problem, Multiobjective duality, Convexity, Generalised convexity.