Decomposition Method for a Class of Monotone Variational Inequality Problems

B. S. He, L. Z. Liao and Hai Yang
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B. S. He: Nanjing University
L. Z. Liao: Hong Kong Baptist University

Journal of Optimization Theory and Applications, 1999, vol. 103, issue 3, No 6, 603-622

Abstract: 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are proper subsets in $$\mathcal{R}^n$$ and $$\mathcal{R}^m$$ , the original augmented Lagrangian method is no longer applicable.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.

Keywords: Monotone variational inequalities; decomposition methods; convergence (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (3)

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DOI: 10.1023/A:1021736008175

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