Mathematical Programming

, Volume 65, Issue 1, pp 1–20

A general cone decomposition theory based on efficiency

  • J. E. Martínez-Legaz
  • A. Seeger
Article

DOI: 10.1007/BF01581687

Cite this article as:
Martínez-Legaz, J.E. & Seeger, A. Mathematical Programming (1994) 65: 1. doi:10.1007/BF01581687

Abstract

LetK1 andK2 be two convex cones in some common vector space. This paper is concerned with the question of finding a ‘good’ decomposition, with respect toK1 andK2, of a given element of the Minkowski sumK1 +K2. 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.

Keywords

Efficient decomposition Moreau decomposition partially ordered vector spaces 

Copyright information

© The Mathematical Programming Society, Inc 1994

Authors and Affiliations

  • J. E. Martínez-Legaz
    • 1
    • 2
  • A. Seeger
    • 2
  1. 1.Departamento d'Economia i d'Història EconòmicaUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Departamento de Matemàtica Aplicada i AnàlisiUniversitat de BarcelonaBarcelonaSpain
  3. 3.Department of Mathematical SciencesKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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