First-order necessary conditions for generalized optimization problems

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

First order optimality conditions for generalized semi-infinite programming problems

In this paper we study first order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend various wellknown constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs take...

On Necessary Conditions for Nonlipschitz Optimization Problems

In this paper, we establish a nessary condition for nonlipschitz constrained optimization problems in terms of Fréchet subdifferentials and normal cones in Asplund spaces.

Convex Generalized Semi-Infinite Programming Problems with Constraint Sets: Necessary Conditions

 We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...

First- and Second-order Necessary Conditions for Control Problems with Constraints

Second-order necessary conditions are developed for an abstract nonsmooth control problem with mixed state-control equality and inequality constraints as well as a constraint of the form G(x, u) e T, where T is a closed convex set of a Banach space with nonempty interior. The inequality constraints g{s, x, u) < 0 depend on a parameter 5 belonging to a compact metric space S. The equality constr...