Abstract

Let K1K_1 and K2K_2 be two nonempty closed convex sets in some normed space (H,∥⋅∥)(H,\|\cdot\|). This paper is concerned with the question of finding a "good" decomposition, with respect to K1K_1 and K2K_2, of a given element of the Minkowski sum K1+K2K_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.

Author information

Contact details are reproduced from the original publication and may be historical.

D. T. Luc

Dép. de Mathématiques, Université d'Avignon, 33 Rue L. Pasteur, 84000 Avignon, France

J. E. Martínez-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

Keywords

  • Least deviation decomposition
  • convex analysis
  • Moreau orthogonal decomposition

Mathematics Subject Classification

41A65; 52A41

References

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Suggested citation

D. T. Luc, J. E. Martínez-Legaz, A. Seeger. “Least Deviation Decomposition with Respect to a Pair of Convex Sets.” Journal of Convex Analysis 6 (1999), No. 1, 115–140. https://doi.org/10.68381/jca06008

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Published by Heldermann Verlag, 1999. Rights now held by Banach Press.