Journal of Convex Analysis 06 (1999), No. 1, 115--140
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. Martinez-Legaz
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 K1 and K2 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 K1 and K2, of a given element of the Minkowski sum K1+K2. 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
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