A general cone decomposition theory based on efficiency

Let K1 and K2 be two convex cones in some common vector space. This paper is concerned with the question of finding a ‘good’ decomposition, with respect to K1 and K2, of a given element of the Minkowski sum K1+K2. The authors propose the criterion of efficiency as a measure for the quality of a decomposition. This criterion allows us to set up a framework from which a general cone decomposition theory is then derived.