Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming

New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem

In recent years, there has been an increasing interest in studying the develpoment of optimality conditions for nondifferentiable multiobjective programming problems. Many authors established and employed some different Kuhn and Tucker type necessary conditions or other type necessary conditions to research optimal solutions; see [1–27] and references therein. In [7], Lai and Ho used the Pareto...

On Optimality Conditions via Weak Subdifferential and Augmented Normal Cone

In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator f...

Optimality Conditions and Duality in Nondifferentiable Minimax Fractional Programming with Generalized Convexity1

We establish sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems involving (F, α, ρ, d)convexity. Subsequently, we apply the optimality conditions to formulate two types of dual problems and prove appropriate duality theorems.

Optimality Conditions and Second-Order Duality for Nondifferentiable Multiobjective Continuous Programming Problems

Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type second-order nondifferentiable multiobjective dual variational problems is constructed. Various duality results for the pair of Mond-Weir type second-order dual variational problems...

Towards Supremum-Sum Subdifferential Calculus Free of Qualification Conditions