Second-order efficient optimality conditions for set-valued vector optimization in terms of asymptotic contingent epiderivatives

We propose a generalized second-order asymptotic contingent epiderivative of a set-valued mapping, study its properties, as well as relations to some second-order contingent epiderivatives, and sufficient conditions for its existence. Then, using these epiderivatives, we investigate set-valued optimization problems with generalized inequality constraints. Both second-order necessary conditions and sufficient conditions for optimality of the Karush-Kuhn-Tucker type are established under the second-order constraint qualification. An application to Mond-Weir and Wolfe duality schemes is also presented. Some remarks and examples are provided to illustrate our results.

Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems

The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived. Based on the concepts of having no duality gap in weak and strong sense, the Wolfe duality theorems for the invex interval-valued nonlinear programming problems are proposed in this paper.

Sufficient Conditions and Duality Theorems for Nondifferentiable Minimax Fractional Programming

We consider nondifferentiable minimax fractional programming problems involving B-(p, r)-invex functions with respect to η and b. Sufficient optimality conditions and duality results for a class of nondifferentiable minimax fractional programming problems are obtained undr B-(p, r)-invexity assumption on objective and constraint functions. Parametric duality, Mond-Weir duality, and Wolfe duality problems may be formulated, and duality results are derived under B-(p, r)-invex functions.