Duality results for interval-valued semiinfinite optimization problems with equilibrium constraints using convexificators
Kin Keung Lai, Shashi Kant Mishra, M. Y. Hassan, Jaya Bisht, Jitendra Kumar Maurya · Journal of Inequalities and Applications · 2022
Abstract This paper deals with the study of interval-valued semiinfinite optimization problems with equilibrium constraints (ISOPEC) using convexificators. First, we formulate Wolfe-type dual problem for (ISOPEC) and establish duality results between the (ISOPEC) and the corresponding Wolfe-type dual under the assumption of $\partial ^{*} $ ∂ ∗ -convexity. Second, we formulate Mond–Weir-type dual problem and propose duality results between the (ISOPEC) and the corresponding Mond–Weir-type dual under the assumption of $\partial ^{*} $ ∂ ∗ -convexity, $\partial ^{*} $ ∂ ∗ -pseudoconvexity, and $\partial ^{*} $ ∂ ∗ -quasiconvexity.