, Volume 65, Issue 1-3, pp 1-20

A general cone decomposition theory based on efficiency

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Abstract

LetK 1 andK 2 be two convex cones in some common vector space. This paper is concerned with the question of finding a ‘good’ decomposition, with respect toK 1 andK 2, of a given element of the Minkowski sumK 1 +K 2. We 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.

Research supported by Dirección General de Investigación Científica y Técnica (DGICYT), under project PS89-0058.