A generalized proximal point algorithm for the nonlinear complementarity problem

A generalized proximal point algorithm for the nonlinear complementarity problem

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Article ID: iaor20052824
Country: France
Volume: 33
Issue: 4
Start Page Number: 447
End Page Number: 479
Publication Date: Oct 1999
Journal: RAIRO Operations Research
Authors: ,
Keywords: complementarity
Abstract:

We consider a generalized proximal point method for solving the nonlinear complementarity problem with monotone operators in Rn. It differs from the classical proximal point method discussed by Rockafellar for the problem of finding zeroes of monotone operators in the use of generalized distances, called φ-divergences, instead of the Euclidean one. These distances play not only a regularization role but also a penalization one, forcing the sequence generated by the method to remain in the interior of the feasible set, so that the method behaves like an interior point one. Under appropriate assumptions on the φ-divergence and the monotone operator we prove that the sequence converges if and only if the problem has solutions, in which case the limit is a solution. If the problem does not have solutions, then the sequence is unbounded. We extend previous results for the proximal point method concerning convex optimization problems.

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