optimality conditions

On a class of nonsmooth composite functions

Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , , , , ,

We discuss in this paper a class of nonsmooth functions which can be represented, in a neighborhood of a considered point, as a composition of a positively homogeneous convex function and a smooth mapping which maps the considered point into the null vector. We argue that this is a sufficiently rich class of functions and … Read more

Optimality Conditions for Vector Optimization with Set-Valued Maps

Categories Generalized Convexity/Monoticity, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , , ,

Based on near convexity, we introduce the concepts of nearly convexlike set-valued maps and nearly semiconvexlike set-valued maps, give some charaterizations of them, and investigate the relationships between them. Then a Farkas-Minkowski type alternative theorem is shown under the assumption of near semiconvexlikeness. By using the alternative theorem and some other lemmas, we establish necessary … Read more