Necessary and sufficient optimality conditions for non-linear unconstrained and constrained optimization problem with interval valued objective function. (September 2020)

• Record Type: Journal Article
• Authors: Rahman, Md Sadikur; Shaikh, Ali Akbar; Bhunia, Asoke Kumar
• Is Part Of: Computers & industrial engineering. Volume 147(2020)
• Publication Date: 2020-09
• Subjects: Interval valued objective function -- Interval valued constraint -- Unconstrained optimization -- Constrained optimization -- Minimizer -- Maximizer -- Necessary optimality conditions; Engineering -- Data processing -- Periodicals; Industrial engineering -- Periodicals; 620.00285
• DOI: 10.1016/j.cie.2020.106634
• Languages: English
• ISSNs: 0360-8352

Abstract

Highlights: We have proposed some definitions local c-r minimizer, global c-r minimizer and c-r convex of interval valued function. Necessary and sufficient conditions for unconstrained optimization problem for interval valued objective. Necessary conditions for constrained optimization problem interval valued objective considered all possible cases. Abstract: In the theory of non-linear constrained optimization problem, the most familiar Karush Kuhn Tucker (KKT) conditions play an important role. Basically, these conditions are necessary optimality conditions of a constrained optimization problem with equality and inequality constraints. The goal of this paper is to introduce the necessary optimality conditions (named as equivalent KKT conditions) of a constrained optimization problem with interval-valued objective function. Depending on the type of objective function and inequality constraints, all possible cases (i.e., objective function interval-valued and constraints are real-valued, objective function and constraints both are interval-valued, the objective function is real-valued and constraints are interval-valued) have been investigated to find the necessary optimality conditions. For this purpose, this paper deals with the necessary and sufficient conditions of unconstrained optimization problem with interval-valued objective function. Also, with the help of interval order relations the definitions of local and global optima of interval-valued function have been proposed. Finally, in order to illustrate the equivalent KKT conditions of the interval-valued constrained optimization problem and also the necessary as well as sufficient conditions of an unconstrained optimization problem, some numerical examples have been considered and solved.