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Erschienen in:
02.11.2021 | Original Research
On sufficiency and duality theorems for nonsmooth semi-infinite mathematical programming problem with equilibrium constraints
Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 5/2022
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Abstract
We aim to establish sufficient optimality conditions in terms of \(\text{ GA }\)-stationary vectors and construct Wolfe and Mond–Weir types dual model in terms of contingent epiderivatives for the global optimal solution of nonsmooth semi-infinite mathematical programming problem with equilibrium constraints in finite-dimensional spaces (\(\text{(NSIMPEC) }\) for short). For this purpose, we provide some fundamental characterizations for the \(\varPsi \)-preinvexity involving the notion of contingent epiderivative and contingent hypoderivative of extended-real-valued function and then some sufficient optimality conditions are obtained for the global optimal solution to such problem. For application purpose, a Mond–Weir and Wolfe types dual model for the problem \(\text{(NSIMPEC) }\) are presented. Especially, some generalized Slater constraint qualifications are proposed and strong/weak duality theorems for the problem \(\text{(NSIMPEC) }\) and its Mond–Weir and Wolfe types dual model are established. Some illustrative examples also proposed for our findings.