In this paper, we propose a homogeneous model for solving monotone mixed complementarity problems over symmetric cones, by extending the results in \cite{YOSHISE04} for standard form of the problems. We show that the extended model inherits the following desirable features: (a) A path exists, 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 every accumulation point of the path gives us a finite certificate proving infeasibility. We also show that the homogeneous model is directly applicable to the primal-dual convex quadratic problems over symmetric cones.
Citation
Vietnam Journal of Mathematics 35 (2007) 541-562