
Journal of Convex Analysis 07 (2000), No. 1, 073094 Copyright Heldermann Verlag 2000 Piecewise Affine Selections for Piecewise Polyhedral Multifunctions and Metric Projections M. Finzel Mathematisches Institut, Universität ErlangenNürnberg, Bismarckstr. 1 1/2, 91054 Erlangen, Germany W. Li Dept. of Mathematics and Statistics, Old Dominion University, Norfolk, VA 235290077, U.S.A. Piecewise polyhedral multifunctions are the setvalued version of piecewise affine functions. We investigate selections of such multifunctions, in particular, the least norm selection and continuous extremal point selections. A special class of piecewise polyhedral multifunctions is the collection of metric projections from the ndimensional euclidean space endowed with a polyhedral norm to a polyhedral subset K. As a consequence, the two types of selections are piecewise affine selections. Moreover, if we consider the euclidean setting endowed with the 1norm, then the metric projection has a piecewise affine and quasilinear extremal point selection when K is a subspace; and if we take the maximum norm then the strict best approximation is a piecewise affine selection for the metric projection onto the polyhedral subset K. [ Fulltextpdf (287 KB)] 