On optimality and duality in interval-valued variational problem with B-(p, r)-invexity

Sardar Vallabhbhai National Institute of Technology, Surat, India.

^* Corresponding author: idmath26@gmail.com

Received: 21 October 2020
Accepted: 30 May 2021

Abstract

In this paper, we consider a class of interval-valued variational optimization problem. We extend the definition of B-(p, r)-invexity which was originally defined for scalar optimization problem to the interval-valued variational problem. The necessary and sufficient optimality conditions for the problem have been established under B-(p, r)-invexity assumptions. An application, showing utility of the sufficiency theorem in real-world problem, has also been provided. In addition to this, for the interval-optimization problem Mond–Weir and Wolfe type duals are presented and related duality theorems have been proved. Non-trivial examples verifying the results have also been presented throughout the paper.