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July  2009, 5(3): 603-613. doi: 10.3934/jimo.2009.5.603

Coerciveness of some merit functions over symmetric cones

Xiao-Hong Liu 1, and  Wei Wu 1,

1. 

Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China, China

Received  February 2008 Revised  January 2009 Published  June 2009

Complementarity problems over symmetric cones (SCCP) can be reformulated as the global minimization of a certain merit function. The coerciveness of the merit function plays an important role in this class of methods. In this paper, we introduce a class of merit functions which contains the Fischer-Burmeister merit function and the natural residual merit function as special cases, and prove the coerciveness of this class of merit functions under some conditions which are strictly weaker than the assumption that the function involving in the SCCP is strongly monotone and Lipschitz continuous. Based on the introduced merit function, we propose another class of merit functions which is an extension of Fukushima-Yamashita merit function. We investigate the coerciveness of the generalized Fukushima-Yamashita merit function under a condition which is strictly weaker than the assumption that the function involving in the SCCP is weakly coercive. The theory of Euclidean Jordan algebras is a basic tool in our analysis.
Keywords: Complementarity problem, Merit function, Symmetric cone, Coerciveness, Euclidean Jordan algebra..
Mathematics Subject Classification: Primary: 90C33; Secondary: 90C2.
Citation: Xiao-Hong Liu, Wei Wu. Coerciveness of some merit functions over symmetric cones. Journal of Industrial and Management Optimization, 2009, 5 (3) : 603-613. doi: 10.3934/jimo.2009.5.603
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