Emil Ernst

STABILITY OF THE SOLUTION SET OF NON-COERCIVE VARIATIONAL INEQUALITIES

In this paper, we study the stability of the solution set of a non-coercive variational inequality with respect to small perturbations of the data involved in the problem. This research is done using well-known tools of convex analysis and the concept of well-positioned convex sets (which is defined and studied).

On the closedness of the algebraic difference of closed convex sets

Abstract We characterize in a reflexive Banach space all the closed convex sets C 1 containing no lines for which the condition C 1 ∞ ∩ C 2 ∞ ={0} ensures the closedness of the algebraic difference C 1 − C 2 for all closed convex sets C 2 . We also answer a closely related problem: determine all the pairs C 1 , C 2 of closed convex sets containing no lines such that the algebraic difference of any sufficiently small uniform perturbations of C 1 and C 2 remains closed. As an application, we state the broadest setting for the strict separation theorem in a reflexive Banach space.

Boundary Half-Strips and the Strong CHIP

When the subdifferential sum rule formula holds for the indicator functions

On the necessity of the Moreau-Rockafellar-Robinson qualification condition in Banach spaces

\iota_C

An approximate Hahn–Banach theorem for positively homogeneous functions

and

Zero Duality Gap for Convex Programs: A Generalization of the Clark–Duffin Theorem

\iota_D

Optimal boundedness criteria for extended-real-valued functions

of two closed convex sets

A converse of the Gale-Klee-Rockafellar theorem: Continuity of convex functions at the boundary of their domains

C

Stability in frictional unilateral elasticity revisited: an application of the theory of semi‐coercive variational inequalities

and

Continuous Sets and Non-Attaining Fuctionals in Reflexive Banach Spaces

D