A continuation method for (strongly) monotone variational inequalities |
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Authors: | Christian Kanzow Houyuan Jiang |
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Affiliation: | (1) Institute of Applied Mathematics, University of Hamburg, Bundesstrasse 55, D-20146 Hamburg, Germany;(2) Department of Mathematics, University of Melbourne, 3052 Parkville, Victoria, Australia |
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Abstract: | We consider the variational inequality problem, denoted by VIP(X, F), whereF is a strongly monotone function and the convex setX is described by some inequality (and possibly equality) constraints. This problem is solved by a continuation (or interior-point) method, which solves a sequence of certain perturbed variational inequality problems. These perturbed problems depend on a parameter > 0. It is shown that the perturbed problems have a unique solution for all values of > 0, and that any sequence generated by the continuation method converges to the unique solution of VIP(X,F) under a well-known linear independence constraint qualification (LICQ). We also discuss the extension of the continuation method to monotone variational inequalities and present some numerical results obtained with a suitable implementation of this method. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V. |
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Keywords: | Variational inequality problems Strongly monotone functions Monotone functions Continuation methods Interior-point methods |
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