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Akiko Yoshise (yoshisesk.tsukuba.ac.jp) Abstract: We study the continuous trajectories for solving monotone nonlinear mixed complementarity problems over symmetric cones. While the analysis in Faybusovich (1997) depends on the optimization theory of convex logbarrier functions, our approach is based on the paper of Monteiro and Pang (1998), where a vast set of conclusions concerning continuous trajectories is shown for monotone complementarity problems over the cone of symmetric positive semidefinite matrices. As an application of the results, we propose a homogeneous model for standard monotone nonlinear complementarity problems over symmetric cones and discuss its theoretical aspects. Consequently, we show the existence of a path having the following properties: (a) The path is bounded and has a trivial starting point without any regularity assumption concerning the existence of feasible or strictly feasible solutions. (b) Any accumulation point of the path is a solution of the homogeneous model. (c) If the original problem is solvable, then every accumulation point of the path gives us a finite solution. (d) If the original problem is strongly infeasible, then, under the assumption of Lipschitz continuity, any accumulation point of the path gives us a finite certificate proving infeasibility. Keywords: Symmetric cone, Complementarity problem, Homogeneous algorithm, Existence of trajectory, Interior point method, Detecting infeasibility Category 1: Linear, Cone and Semidefinite Programming (Other ) Category 2: Complementarity and Variational Inequalities Citation: SIAM Journal on Optimization 17 (2006) 1129  1153 Download: Entry Submitted: 08/09/2004 Modify/Update this entry  
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