Publications

The paper is devoted to establishing relationships between global and local monotonicity, as well as their maximality versions, for single-valued and set-valued mappings between finite-dimensional and infinite-dimensional spaces. We first show that for single-valued operators with convex domains in locally convex topological spaces, their continuity ensures that their global monotonicity agrees with the local one around any point of the graph. This also holds for set-valued mappings defined on the real line under a certain connectedness condition. The situation is different for set-valued operators in multidimensional spaces as demonstrated by an example of locally monotone operator on the plane that is not globally monotone. Finally, we invoke coderivative criteria from variational analysis to characterize both global and local maximal monotonicity of set-valued operators in Hilbert spaces to verify the equivalence between these monotonicity properties under the closed-graph and global hypomonotonicity assumptions.

We introduce and study a notion of co-radiantness for set-valued mappings between nonnegative orthants of Euclidean spaces. We analyze them from an abstract convexity perspective. Our main results consist in representations, in terms of intersections of graphs, of the increasing co-radiant mappings that take closed normal values, by means of elementary members in the class of such mappings.

We study an approximation method for sets and functions which erases corners but keeps smooth parts. Basic properties of such a method are pointed out in a general and simple way. Several convergence results are provided, essentially in the framework of variational analysis.

This Special Issue of the Journal ‘Optimization’ is dedicated to the ‘International Seminar on Optimization and Related Areas’ (ISORA), which was held at the Instituto de Matematica y Ciencias Afin...

Fenchel subdifferential operators of lower semicontinuous proper convex functions on real Banach spaces are classically characterized as those operators that are maximally cyclically monotone or, equivalently, maximally monotone and cyclically monotone. This paper presents an alternative characterization, which does not involve cyclic monotonicity. In the case of subdifferential operators of sublinear functions, the new characterization substantially simplifies. Dually, the new characterization of normal cone operators is very simple, too.

The paper provides a new subdifferential characterization for Motzkin decomposable (convex) functions. This characterization leads to diverse stability properties for such a decomposability for operations like addition and composition.

A forthcoming special issue of Journal of Global Optimization contains a number of articles that may be interesting to economic theorists. Table of Contents: A.M. Bagirov and A.M. Rubinov Global optimization of marginal functions with applications to economic equilibrium K. Cechlarova, M. Dahm and V. Lacko Efficiency and stability in a discrete model of country formation I.V. Evstigneev and S.D. Flam Sharing Nonconvex Costs M.E. Jerrell and W.A. Campione Global optimization of econometric functions R. John The concave nontransitive consumer C. Le Van, F.H. Page, Jr. and M.H. Wooders Arbitrage and Equilibrium in Economies with Externalities G.G. Malcolm and B.S. Mordukhovich Pareto optimality in nonconvex economies with infinite-dimensional commodity spaces A. Soubeyran and H. Stahn Price Behaviors on Networks: Some General Results for Two-way Networks A. Villar On the efficiency of market equilibrium in production economies

Let g be a strictly convex function on an evenly convex set X⊂Rn with nonempty interior. Assuming that g is differentiable on intX, we consider the Bregman distance Dg associated with g. Given a set T ⊂Rn, whose elements are called sites, and a particular site s, the farthest g-Bregman Voronoi cell of s, denoted by FTg(s), consists of all points that are farther from s than from any other site with respect to Dg. In this paper we study farthest g-Bregman Voronoi cells; in particular, we characterize those sets that can be written as FTg(s) for some T⊂Rn and some s∈T.