Decomposition through formalization in a product space

Abstract

When an optimization problem is posed in a product space it is classical to decompose this problem. The goal of this paper is to show how such an approach can be used when the problem to be solved is not naturally posed in a product space. By associating systematically to this problem an equivalent one posed in ann-fold cartesian product space, we obtain by decomposition of the latter both a splitting of operators and a desintegration of constraints for the former. Applications to three rather classical mathematical programming problems are given.