Non-differentiable multiobjective programming under generalised functions Online publication date: Fri, 29-May-2015
by Pallavi Kharbanda; Divya Agarwal; Deepa Sinha
International Journal of Operational Research (IJOR), Vol. 23, No. 3, 2015
Abstract: In this paper, we consider a nonlinear multiobjective programming problem where functions involved are non-differentiable. The use of directional derivative in association with a hypothesis of an invex kind on the set has been of much interest in the recent past. Recently under preinvexity assumptions on fi′(xo;ηi(x,xo)) and g′j (xo;θj(x,xo)), necessary and sufficient optimality conditions for a non-smooth multiobjective optimisation problem under generalised class of dI-V-type I functions have been derived. Working in this direction, we introduce a new class of (φ, dI)-V-type I functions and illustrate through various non-trivial examples that this class is non-empty and extends some known classes introduced in the literature. Also, we obtain sufficient optimality conditions to enable a feasible solution of the primal problem to be its weak efficient/efficient solution. Then through an example, we illustrate the relevance of the sufficient optimality theorem obtained to get the efficient solution of the problem. Further, we formulate Wolfe type and Mond-Weir type multiobjective dual programs and establish various duality theorems under this newly introduced class of functions.
Online publication date: Fri, 29-May-2015
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Operational Research (IJOR):
Login with your Inderscience username and password:
Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.
If you still need assistance, please email email@example.com