Title: Duality for non-differentiable multi-objective semi-infinite programming for higher order invex functions

Authors: Promila Kumar; Jyoti

Addresses: Department of Mathematics, Gargi College (University of Delhi), New Delhi 110049, India ' Department of Mathematics, University of Delhi, Delhi 110007, India

Abstract: This paper deals with non-differentiable multi-objective semi-infinite programming problem. It is a problem of simultaneous minimisation of finitely many scalar valued functions subject to an arbitrary (possibly infinite) set of constraints. Non-differentiability enters, due to the square root of a quadratic form which appears in the objective functional. Concept of efficiency of order m has been extended to the above stated problem. In order to study this new solution concept, the notion of ρ-invexity of order m is also proposed which is utilised to establish sufficient optimality conditions for the non-differentiable multi-objective semi-infinite programming problem. Mond-Weir type of dual is proposed for which weak, strong and strict converse duality theorems are established.

Keywords: optimality; duality; semi-infinite programming; non-differentiable programming; ρ-invexity of order m.

DOI: 10.1504/IJMOR.2018.092105

International Journal of Mathematics in Operational Research, 2018 Vol.12 No.4, pp.457 - 470

Received: 14 Oct 2015
Accepted: 28 Oct 2016
Published online: 04 Jun 2018 *

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