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Journal of Convex Analysis, Vol. 6, No. 1, pp. 115-140 (1999)
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Least Deviation Decomposition with Respect to a Pair of Convex Sets

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D. T. Luc and J. E. Martinez-Legaz and A. Seeger

Universite d'Avignon, Departement de Mathematiques, 33, rue L. Pasteur, 84000 Avignon, France, dtluc@univ-avignon.fr and Universitat Autonoma de Barcelona, CODE and Departament d'Economia i d'Historia Economica, 08193 Bellaterra, Spain, JuanEnrique.Martinez@uab.es and King Fahd University of Petroleum and Minerals, Department of Mathematical Sciences, Dhahran 31261, Saudi Arabia, alberto.seeger@univ-avignon.fr

**Abstract:** Let $K_1$ and $K_2$ be two nonempty closed convex sets in some normed space $(H,\Vert \cdot \Vert )$. This paper is concerned with the question of finding a "good" decomposition, with respect to $K_1$ and $K_2$, of a given element of the Minkowski sum $K_1+K_2$. We introduce and discuss the concept of least deviation decomposition. This concept is an extension of the Moreau orthogonal decomposition with respect to a pair of mutually polar cones. Techniques of convex analysis are applied to obtain some sensitivity and duality results related to the decomposition problem.

**Keywords:** Least deviation decomposition, convex analysis, Moreau orthogonal decomposition

**Classification (MSC2000):** 41A65, 52A41

**Full text of the article:**

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