ISSN:
1436-4646
Keywords:
Complementarity problem
;
continuation method
;
P-function
;
homeomorphism
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract The complementarity problem with a nonlinear continuous mappingf from the nonnegative orthantR + n ofR n intoR n can be written as the system of equationsF(x, y) = 0 and(x, y) ∈ R + 2n , whereF denotes the mapping from the nonnegative orthantR + 2n ofR 2n intoR + n × Rn defined byF(x, y) = (x 1y1,⋯,xnyn, f1(x) − y1,⋯, fn(x) − yn) for every(x, y) ∈ R + 2n . Under the assumption thatf is a uniformP-function, this paper establishes that the mappingF is a homeomorphism ofR + 2n ontoR + n × Rn. This result provides a theoretical basis for a new continuation method of tracing the solution curve of the one parameter family of systems of equationsF(x, y) = tF(x 0, y0) and(x, y) ∈ R + 2n from an arbitrary initial point(x 0, y0) ∈ R + 2n witht = 1 until the parametert attains 0. This approach is an extension of the one used in the polynomially bounded algorithm recently given by Kojima, Mizuno and Yoshise for solving linear complementarity problems with positive semi-definite matrices.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01582283
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