The results presented in this book originate from the last decade research work of the author
in the? eld of duality theory in convex optimization. The reputation of duality in the …

The paper concerns the study of new classes of parametric optimization problems of the so-
called infinite programming that are generally defined on infinite-dimensional spaces of …

In this paper we present a survey of generalizations of the celebrated Farkas's lemma,
starting from systems of linear inequalities to a broad variety of non-linear systems. We focus …

For an inequality system defined by a possibly infinite family of proper functions (not
necessarily lower semicontinuous), we introduce some new notions of constraint …

The problem to find a best solution within the set of optimal solutions of a convex
optimization problem is modeled as a bilevel programming problem. It is shown that …

For an inequality system defined by an infinite family of proper convex functions (not
necessarily lower semicontinuous), we introduce some new notions of constraint …

The paper is devoted to the study of a new class of optimization problems with objectives
given as differences of convex (DC) functions and constraints described by infinitely many …

The closedness type regularity conditions have proven during the last decade to be viable
alternatives to their more restrictive interiority type counterparts, in both convex optimization …

In this paper we discuss the simple bilevel programming problem (SBP) and its extension,
the simple mathematical programming problem under equilibrium constraints (SMPEC) …

In this paper we present two Fenchel-type dual problems for a DC (difference of convex
functions) optimization primal one. They have been built by means of the c-conjugation …