Duality without constraint qualification in nonsmooth optimization

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...

Mixed Duality for Nonsmooth Multiobjective Fractional Programming without a Constraint Qualification

New Constraint Qualification and Conjugate Duality for Composed Convex Optimization Problems

We present a new constraint qualification which guarantees strong duality between a cone-constrained convex optimization problem and its Fenchel-Lagrange dual. This result is applied to a convex optimization problem having, for a given nonempty convex cone K , as objective function a K-convex function postcomposed with a K-increasing convex function. For this so-called composed convex optimizat...

Necessary and Sufficient Constraint Qualification for Surrogate Duality

In mathematical programming, constraint qualifications are essential elements for duality theory. Recently, necessary and sufficient constraint qualifications for Lagrange duality results have been investigated. Also, surrogate duality enables one to replace the problem by a simpler one in which the constraint function is a scalar one. However, as far as we know, a necessary and sufficient cons...

Convex Inequalities without Constraint Qualification nor Closedness Condition, and Their Applications in Optimization

Given two convex lower semicontinuous extended real valued functions F and h de…ned on locally convex spaces, we provide a dual transcription of the relation