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An interior point method for the nonlinear complementarity problem

โœ Scribed by Alfredo Noel Iusem

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
664 KB
Volume
24
Category
Article
ISSN
0168-9274

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โœฆ Synopsis

We present an interior point method for the nonlinear complementarity problem which converges, whenever the problem has solutions, for any paramonotone operator (i.e., monotone and such that (F(x) -F(y), x-y) = 0 implies F(x) = F(y)). The iterative step consists of easily computable closed formulae, up to a finite search for a real parameter. Convergence of the algorithm results from its reduction to an interior point method for variational inequalities using Bregman functions, whose iterative step requires a similar finite search plus the solution of a nonlinear equation in one real variable. As an intermediate step in the reduction, we simplify the method for variational inequalities, replacing the solution of the nonlinear equation by a second finite search for another real parameter, which is finally replaced by a closed formula in the case of nonlinear complementarity problems.

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