Recent Issues Volume 37 1 2 3 4 Volume 36 1 2 3 4 Volume 35 1 2 3 4 Volume 34 1 2 3 4 Volume 33 1 2 3 4 Past Issues The Journal Cover Aims and Scope Subscription Information Editorial Board Instructions for Author Contact Us Related Links

Vietnam Journal of Mathematics 35:4(2007) 541-561  A Homogeneous Model for Mixed Complementarity Problems over Symmetric Cones Yedong Lin and Akiko Yoshise Abstract.  In this paper, we propose a homogeneous model for solving monotone mixed complementarity problems over symmetric cones, by extending the results in [11] 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, under the assumption of Lipschitz continuity, any 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.   2000 Mathematics Subject Classification: 90C22, 90C25, 90C33, 65K05, 46N10. Keywords: Complementarity problem, nonlinear optimization, optimality condition, symmetric cone, Euclidean Jordan algebra, homogeneous algorithm, interior point method, detecting infeasibility.

Vietnam Academy of Science and Technology & Vietnamese Mathematical Society © Copyright 2009 Vietnam Journal of Mathematics. All rights reserved.