A continuation method for (strongly) monotone variational inequalities

被引：0
作者：
Christian Kanzow
Houyuan Jiang
机构：
[1] University of Hamburg,Institute of Applied Mathematics
[2] University of Melbourne,Department of Mathematics
来源：
Mathematical Programming | 1998年 / 81卷
关键词：
Variational inequality problems; Strongly monotone functions; Monotone functions; Continuation methods; Interior-point methods;
D O I：
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中图分类号：
学科分类号：
摘要：
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 parameterμ > 0. It is shown that the perturbed problems have a unique solution for all values ofμ > 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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页码：103 / 125
页数：22
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