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Some P-Properties for Nonlinear Transformations on Euclidean Jordan Algebras

Department of Mathematical Sciences, Loyola College in Maryland, Baltimore, Maryland 21210
Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250
jtao{at}loyola.edu
gowda{at}math.umbc.edu, www.math.umbc.edu/~gowda

In this article, we introduce the concepts of P and P₀ properties for a nonlinear transformation defined on a Euclidean Jordan algebra and study existence of solution in the associated complementarity problems. In particular, we show, in this general setting, that if a transformation has the P₀ and R₀ properties, then all associated complementarity problems have solutions. We also describe a necessary condition for a transformation to have the (global) uniqueness of solution property.

Key Words: Euclidean Jordan algebra; P-property; complementarity problem; globally uniquely solvable property
History: Received: March 1, 2004; revision received: November 16, 2004;revision received: February 3, 2005;

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