Linear Complementarity Problems over Symmetric Cones: Characterization of Q b -transformations and Existence Results

Julio López (), Rúben López () and Héctor C. Ramírez ()
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Julio López: Universidad Técnica Federico Santa María
Rúben López: Universidad Católica de la Santísima Concepción
Héctor C. Ramírez: Universidad de Chile

Journal of Optimization Theory and Applications, 2013, vol. 159, issue 3, No 12, 768 pages

Abstract: Abstract This paper is devoted to the study of the symmetric cone linear complementarity problem (SCLCP). Specifically, our aim is to characterize the class of linear transformations for which the SCLCP has always a nonempty and bounded solution set in terms of larger classes. For this, we introduce a couple of new classes of linear transformations in this SCLCP context. Then, we study them for concrete particular instances (such as second-order and semidefinite linear complementarity problems) and for specific examples (Lyapunov, Stein functions, among others). This naturally permits to establish coercive and noncoercive existence results for SCLCPs.

Keywords: Euclidean Jordan algebra; Linear complementarity problem; Symmetric cone; Q b -transformation; Q-transformation; García’s transformation (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0116-4

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