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

Tamanna Yadav,S.K Gupta

doi:10.1051/ro/2021064

Tamanna Yadav, S.K Gupta

Open Access

https://doi.org/10.1051/ro/2021064

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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 modelsvizMond-Weir, Wolfe and Schaible are presented and then usual duality results are proved using higher-order (K×Q) − (ℱ,α,ρ,d)-typeIconvexity 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.

Highlights

A semi-infinite model (SIM) is an optimization problem having finite number of variables with the infinite number of constraints
In 1962, SIM is named by Charnes et al [6], in which a survey of SIM mainly about a linear model and duality results with convex property have been done
Some important theorems for the linear model have been generalized using the pairing of finite space of sequences and vector space of finite dimension

Summary

Introduction

A semi-infinite model (SIM) is an optimization problem having finite number of variables with the infinite number of constraints. For SIM, considering the concept of convexificators, Pandey and Mishra [24, 25] have proposed necessary as well as sufficient optimality conditions They formulated Mond-Weir and Wolfe type duals, and proved related theorems with the help of ∂∗-convexity\generalized convexity. Due to the presence of support functions in each numerator and denominator of the objective function and in each constraint, the problem becomes non-smooth This generalizes all the existing semi-infinite models and gives infinitely many optimization problems since it involves arbitrary cones. The conclusion with future scope is given

Preliminaries

Mond-Weir type dual

Wolfe type dual

Schaible type dual

Conclusion