DOMINATING SETS FOR CONVEX-FUNCTIONS WITH SOME APPLICATIONS

A number of optimization methods require as a first step the construct ion of a dominating set (a set containing an optimal solution) enjoyin g properties such as compactness or convexity, In this paper, we addre ss the problem of constructing dominating sets for problems whose obje ctive is a componentwise nondecreasing function of (possibly an infini te number of) convex functions, and we show how to obtain a convex dom inating set in terms of dominating sets of simpler problems. The appli cability of the results obtained is illustrated with the statement of new localization results in the fields of linear regression and locati on.