On Necessary Conditions for Nonlipschitz Optimization Problems

Optimality Conditions and a Smoothing Trust Region Newton Method for NonLipschitz Optimization

Abstract. Regularized minimization problems with nonconvex, nonsmooth, perhaps nonLipschitz penalty functions have attracted considerable attention in recent years, owing to their wide applications in image restoration, signal reconstruction and variable selection. In this paper, we derive affine-scaled second order necessary and sufficient conditions for local minimizers of such minimization p...

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

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

In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are Lipschitz near the optimal solution. Necessary optimality conditions and constraint qualifications in terms of Michel-Penot subdifferential are given.

Regularity Conditions for Non-Differentiable Infinite Programming Problems using Michel-Penot Subdifferential

In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are locally Lipschitz‎. ‎Necessary optimality conditions and regularity conditions are given‎. ‎Our approach are based on the Michel-Penot subdifferential.

Optimality conditions for approximate solutions of vector optimization problems with variable ordering structures

‎We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces‎. ‎Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...