Continuity concepts for set-valued functions and a fundamental duality formula for set-valued optimization

Existence and Lagrangian Duality .for Maximizations of Set-Valued Functions

The maximization with respect to a cone of a set-valued function into possibly infinite dimensions is defined; some existence results are established; and a Lagrangian duality theory is developed.

Approximate Fenchel-Lagrangian Duality for Constrained Set-Valued Optimization Problems

In this article, we construct a Fenchel-Lagrangian ε-dual problem for set-valued optimization problems by using the perturbation methods. Some relationships between the solutions of the primal and the dual problems are discussed. Moreover, an ε-saddle point theorem is proved.

K-epiderivatives for set-valued functions and optimization

Monotone set-valued functions defined by set-valued Choquet integrals

In this paper, some properties of the monotone set-valued function defined by the set-valued Choquet integral are discussed. It is shown that several important structural characteristics of the original set function, such as null-additivity, strong order continuity, property(S) and pseudometric generating property, etc., are preserved by the new set-valued function. It is also shown that integr...

Discrete Set-Valued Continuity and Interpolation

The main question of this talk is to retrieve some continuity properties on (discrete) T0-Alexandroff spaces. One possible application, which will guide us, is the construction of the so-called "tree of shapes" (intuitively, the tree of level lines). This tree, which should allow to process in the same way maxima and minima, faces quite a number of theoretical difficulties that we propose to so...