On duality theory for multiobjective semi-infinite fractional optimization model using higher order convexity

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247 667, India.

^* Corresponding author: skgiitr@gmail.com

Received: 9 October 2020
Accepted: 17 April 2021

Abstract

In the article, a semi-infinite fractional optimization model having multiple objectives is first formulated. Due to the presence of support functions in each numerator and denominator with constraints, the model so constructed is also non-smooth. Further, three different types of dual models viz Mond-Weir, Wolfe and Schaible are presented and then usual duality results are proved using higher-order (K × Q) − (ℱ, α, ρ, d)-type I convexity assumptions. To show the existence of such generalized convex functions, a nontrivial example has also been exemplified. Moreover, numerical examples have been illustrated at suitable places to justify various results presented in the paper. The formulation and duality results discussed also generalize the well known results appeared in the literature.