Dominating sets for convex functions with some applications

Abstract

A number of optimization methods require as a rst step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity. In this note we address the problem of constructing dominating sets for problems whose ob jective is a componentwise nondecreasing function of (possibly an in nite number of ) convex functions, and we show how to obtain a convex dominating set in terms of dominating sets of simpler problems. The applicability of the results obtained is illustrated with the statement of new localization results in the elds of Linear Regression and Location.