
Journal of Convex Analysis 06 (1999), No. 1, 115140 Copyright Heldermann Verlag 1999 Least Deviation Decomposition with Respect to a Pair of Convex Sets D. T. Luc Dép. de Mathématiques, Université d'Avignon, 33 Rue L. Pasteur, 84000 Avignon, France J. E. MartinezLegaz Dep. d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona, 08193 Bellaterra  Barcelona, Spain Alberto Seeger King Fahd University of Petroleum and Minerals, Dept. of Mathematical Sciences, Dhahran 31261, Saudi Arabia Let K_{1} and K_{2} be two nonempty closed convex sets in some normed space (H,' . '). 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. MSC: 41A65; 52A41 [ Fulltextpdf (313 KB)] 