Set-valued optimization is a vibrant and expanding branch of applied mathematics that
deals with optimization problems where the objective map and/or the constraint maps are …

The continuous and increasing interest concerning vector optimization perceptible in the
research community, where contributions dealing with the theory of duality abound lately …

With the republication of our book, first published in 1988, we would like to recall how it all
started. Mordecai Avriel worked on nonlinear programming, where convexity plays a major …

The known Lagrange multiplier rule is extended to set-valued constrained optimization
problems using the contingent epiderivative as differentiability notion. A necessary optimality …

In this paper,(α, φ, Q)-invexity is introduced, where α: X× X→ int R m+, φ: X× X→ X, X is a
Banach space, Q is a convex cone of R m. This unifies the properties of many classes of …

This paper examines nonsmooth constrained multi-objective optimization problems where
the objective function and the constraints are compositions of convex functions, and locally …

Necessary and sufficient optimality conditions are given for various optimality notions in set-
valued optimization. These optimality conditions are given by employing the generalized …

In recent years second-order sufficient conditions of an isolated local minimizer for convex
composite optimization problems have been established. In this paper, second-order …

In this paper, we study different classes of generalized convex/quasiconvex set-valued
maps, defined by means of the l-type and u-type preorder relations, currently used in set …

After a survey of the main definitions of generalized convex and generalized invex vector
functions, some other broad classes of generalized invex vector functions are introduced …