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Vietnam Journal of Mathematics 35:4(2007)
541-561
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A Homogeneous Model for Mixed
Complementarity Problems over Symmetric Cones
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Yedong Lin and
Akiko Yoshise
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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.
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2000 Mathematics Subject Classification: 90C22, 90C25,
90C33, 65K05, 46N10.
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Keywords: Complementarity problem, nonlinear
optimization, optimality condition, symmetric cone, Euclidean Jordan
algebra, homogeneous algorithm, interior point method, detecting
infeasibility.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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