A study on vector variational-like inequalities using convexificators and application to its bi-level form

Gayatri Pany; Ram N. Mohapatra

doi:10.3934/jimo.2021161

Article Contents

2022, Volume 18, Issue 6: 4333-4350. Doi: 10.3934/jimo.2021161

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A study on vector variational-like inequalities using convexificators and application to its bi-level form

Gayatri Pany^, and
Ram N. Mohapatra

Department of Mathematics, University of Central Florida, 4000 Central Blvd, P.O Box 161364, Orlando, Florida 32816-1364, USA

^* Corresponding author: Gayatri Pany
^* Corresponding author: Gayatri Pany

Received: October 2020

Revised: July 2021

Early access: September 2021

Published: November 2022

The first author is supported by grant from Mohapatra Family Foundation and the College of Graduate Studies of the University of Central Florida.

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Abstract

This paper deals with the weak versions of the vector variational-like inequalities, namely Stampacchia and Minty type under invexity in the framework of convexificators. The connection between both the problems along with the link to vector optimization problem are analyzed. An application to nonconvex mathematical programming has also been presented. Further, the bi-level version of these problems is formulated and a procedure to obtain the solution involving the auxiliary principle technique is described in detail. We have shown that the iterative algorithm with the help of which we get the approximate solution converges strongly to the exact solution of the problem.

Keywords:

Convexificator,
vector variational-like inequality,
generalized invexity,
bi-level vector variational-like inequality.

Mathematics Subject Classification: Primary: 90C56, 47J20; Secondary: 90C33.

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