Title: Non-smooth multiobjective programming problem involving (d_I - ρ - σ)-V-type I functions

Authors: Pallavi Kharbanda; Divya Agarwal; Deepa Sinha

Addresses: Centre for Mathematical Sciences, Banasthali University, Tonk District, Rajasthan-304022, India ' Department of Applied Sciences and Humanities, ITM University, Sector 23 A, Gurgaon-122017, Haryana, India ' Department of Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi-110021, India

Abstract: In this paper, we consider a multiobjective optimisation problem where the objective and constraint functions involved are non-differentiable. We introduce a new class of functions namely (d_I - ρ - σ)-V-type I functions and illustrate through non-trivial examples that the class introduced is non-empty. We then obtain sufficient optimality conditions under the newly introduced class of functions and derive various weak, strong, converse and strict converse duality results for Wolfe type and Mond-Weir type dual programmes in order to relate the efficient and weak efficient solutions of primal and dual problems.

Keywords: multiobjective optimisation; directional derivative; efficiency; d_I-V-type I functions; non-smooth multiobjective programming.

DOI: 10.1504/IJOR.2014.064019

International Journal of Operational Research, 2014 Vol.21 No.1, pp.1 - 24

Received: 27 Sep 2012
Accepted: 21 Dec 2012
Published online: 30 Aug 2014 *

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