Optimality and duality without a constraint qualification for minimax programming

Duality without constraint qualification in nonsmooth optimization

We are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. In order to obtain our main results, we give the definitions of the generalized convex functions based on the generalized directional derivative. Under the above generalized convexity assumptions, sufficient and necessary conditions for optimality are given without the need of a constraint qualifi...

Optimality and Duality for Minimax Fractional Semi-Infinite Programming

The purpose of this paper is to consider a class of nonsmooth minimax fractional semi-infinite programming problem. Based on the concept of H − tangent derivative, a new generalization of convexity, namely generalized uniform ( , ) H B ρ − invexity, is defined for this problem. For such semi-infinite programming problem, several sufficient optimality conditions are established and proved by uti...

Mixed Duality for Nonsmooth Multiobjective Fractional Programming without a Constraint Qualification

On Sequential Optimality Conditions without Constraint Qualifications for Nonlinear Programming with Nonsmooth Convex Objective Functions

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...

A Practical Optimality Condition without Constraint Qualiications for Nonlinear Programming

A new optimality condition for minimization with general constraints is introduced. Unlike the KKT conditions, this condition is satissed by local minimizers of nonlinear programming problems, independently of constraint qualiications. The new condition implies, and is strictly stronger than, Fritz-John optimality conditions. Suu-ciency for convex programming is proved.