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A continuation method for (strongly) monotone variational inequalities. (English) Zbl 0920.90131
Summary: We consider the variational inequality problem, denoted by \(\text{VIP}(X, F)\), where \(F\) is a strongly monotone function and the convex set \(X\) 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 \(\mu>0\). It is shown that the perturbed problems have a unique solution for all values of \(\mu> 0\), and that any sequence generated by the continuation method converges to the unique solution of \(\text{VIP}(X,F)\) 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.

MSC:
90C30 Nonlinear programming
49J40 Variational inequalities
Software:
MCPLIB; PATH Solver
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