Duality results for interval-valued pseudoconvex optimization problem with equilibrium constraints with applications

Abstract

This paper is devoted to constructing Wolfe and Mond-Weir dual models for interval-valued pseudoconvex optimization problem with equilibrium constraints, as well as providing weak and strong duality theorems for the same using the notion of contingent epiderivatives with pseudoconvex functions in real Banach spaces. First, we introduce the Mangasarian-Fromovitz type regularity condition and the two Wolfe and Mond-Weir dual models to such problem. Second, under suitable assumptions on the pseudoconvexity of objective and constraint functions, weak and strong duality theorems for the interval-valued pseudoconvex optimization problem with equilibrium constraints and its Mond-Weir and Wolfe dual problems are derived. An application of the obtained results for the GA-stationary vector to such interval-valued pseudoconvex optimization problem on sufficient optimality is presented. We also give several examples that illustrate our results in the paper. Keywords Interval-valued pseudoconvex optimization problem with equilibrium constraints • Wolfe type dual • Mond-Weir type dual • Optimality conditions • Subdifferentials • Pseudoconvex functions Mathematics Subject Classification 90C46 • 49J52 • 45N15

Generalized-Hukuhara Subgradient and its Application in Optimization Problem with Interval-valued Functions

“…The authors of [1,2,22,32,33] proposed various optimality and duality conditions for nonsmooth IOPs converting them into real-valued multiobjective optimization. However, in this approach, one needs the closed-form of boundary functions of the interval-valued objective and constrained functions as readily available, which is practically difficult.…”

Optimality conditions and duality results for generalized-Hukuhara subdifferentiable preinvex vector interval optimization problems

“…Bhurjee and Padhan [21] discussed the interval optimization problem when both the objective function and constraint function are non-differentiable, and proposed the corresponding dual problem. Reference [22][23][24][25][26] studied non-smooth interval optimization problems by transforming them into real-valued multi-objective optimization problems, and then proposed corresponding optimality conditions and duality results. However, to the best of our knowledge, there is currently limited research on the gH-subdifferential interval optimization problem, and also the (VIOP) under preinvexity has not been studied yet.…”

“…Inspired by references [21,23,26,27] and the related literatures, this paper will study non-differentiable preinvex (VIOP) under the gH-difference, as well as dual problems of Mond-Wier and Wolfe by the means of gH-subdifferential. In Section 2, some basic definitions are given.…”

Sufficient conditions for the optimal control problems with interval-valued objective function in admissible orders

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