In this work we give an extension of the Brondsted-Rockafellar Theorem, and some of its important consequences, to proper convex lower-semicontinuous epi-pointed functions defined in locally convex spaces. We use a new ...

We give new characterizations for the subdifferential of the supremum of an arbitrary family of convex functions, dropping out the standard assumptions of compactness of the index set and upper semi-continuity of the ...

We consider an implicit iterative method in convex programming which combines inexact variants of the proximal point algorithm, with parametric penalty functions. We investigate a multiplier sequence which is explicitly ...

We consider a nonlinear convex program. Under some general hy-potheses, we prove that approximate solutions obtained by exponential penalty converge toward a particular solution of the original convex program as the penalty ...

Stochastic convex optimization, by which the objective is the expectation of a random convex function, is an important and widely used method with numerous applications in machine learning, statistics, operations research, ...

In this paper we establish general formulas for the subdifferential of the pointwise supremum of convex functions, which cover and unify both the compact continuous and the non-compact non-continuous settings. From the ...

Many problems of theoretical and practical interest involve finding a convex or concave function.For instance, optimization problems such as finding the projection on the convex functions in $H^k(Omega)$, or some problems ...

A coloring of the vertices of a graph G is convex if, for each assigned color d, the vertices with color d induce a connected subgraph of G. We address the convex recoloring problem, defined as follows. Given a graph G and ...