Mangasarian-Fromovitz and Zangwill Conditions For Non-Smooth Infinite Optimization problems in Banach Spaces

Quasi-Gap and Gap Functions for Non-Smooth Multi-Objective Semi-Infinite Optimization Problems

In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced ...

Perturbed optimization in Banach spaces III: Semi-infinite optimization

This paper is devoted to the study of perturbed semi-infinite optimization problems, i.e., minimization over ]R with an infinite number of inequality constraints. We obtain the second-order expansion of the optimal value function and the first-order expansion of approximate optimal solutions in two cases: (i) when the number of binding constraints is finite and (ii) when the inequality constrai...

Lagrangian conditions for vector optimization in Banach spaces

We consider vector optimization problems on Banach spaces without convexity assumptions. Under the assumption that the objective function is locally Lipschitz we derive Lagrangian necessary conditions on the basis of Mordukhovich subdifferential and the approximate subdifferential by Ioffe using a non-convex scalarization scheme. Finally, we apply the results for deriving necessary conditions f...

Optimality Conditions for Disjunctive Optimization in Reflexive Banach Spaces

Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification

The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian–Fromovitz Constraint Qualification, we establish re...

Non-Lipschitz Semi-Infinite Optimization Problems Involving Local Cone Approximation

In this paper we study the nonsmooth semi-infinite programming problem with inequality constraints. First, we consider the notions of local cone approximation $Lambda$ and $Lambda$-subdifferential. Then, we derive the Karush-Kuhn-Tucker optimality conditions under the Abadie and the Guignard constraint qualifications.