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

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We establish Fritz John necessary conditions for local weak efficient solutions of vector equilibrium problems with constraints in terms of contingent derivatives. Under suitable constraint qualifications, Karush–Kuhn–Tucker necessary conditions for those solutions are investigated.

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