Decomposition Method for a Class of Monotone Variational Inequality Problems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Decomposition Method for a Class of Monotone Variational Inequality Problems

Authors:

Institution:

(1) Department of Mathematics, Nanjing University, Nanjing, P. R. China;(2) Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong;(3) Department of Civil Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Abstract:

In the solution of the monotone variational inequality problem VI( OHgr

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$\mathcal{Y}$ are proper subsets in $\mathcal{R}^n$ and $\mathcal{R}^m$ , the original augmented Lagrangian method is no longer applicable.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

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