Least Deviation Decomposition with Respect to a Pair of Convex Sets

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.