ISSN:
1573-2878
Keywords:
Monotone variational inequalities
;
decomposition methods
;
convergence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In the solution of the monotone variational inequality problem VI(Ω, F), with $$u = \left[ {\begin{array}{*{20}c} x \\ y \\ \end{array} } \right],Fu = \left[ {\begin{array}{*{20}c} {fx - ATy} \\ {Ax - b} \\ \end{array} } \right],\Omega = \mathcal{X} \times \mathcal{Y},$$ the augmented Lagrangian method (a decomposition method) is advantageous and effective when $$\mathcal{X} = \mathcal{R}^m$$ . For some problems of interest, where both the constraint sets $$\mathcal{X}$$ and $$\mathcal{Y}$$ are proper subsets in $$\mathcal{R}^n$$ and $$\mathcal{R}^m$$ , the original augmented Lagrangian method is no longer applicable. For this class of variational inequality problems, we introduce a decomposition method and prove its convergence. Promising numerical results are presented, indicating the effectiveness of the proposed method.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1021736008175
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