Decomposition method for a class of monotone variational inequality problems
A monotone variational inequality is considered on a set \(\Omega= X\times Y\), where \(X\) and \(Y\) are constraints sets. The classical augmented Lagrangian method is advantageous and effective when \(Y= \mathbb{R}^m\). For some problems of interest, such as minimax problems, where both \(X\) and \(Y\) are proper subsets in \(\mathbb{R}^n\) and \(\mathbb{R}^m\), the original augmented Lagrangian method is no longer applicable. A new decomposition method is introduced for that case and its convergence is demonstrated. If \(Y= \mathbb{R}^m\), the new method reduces to the augmented Lagrangian method. Numerical results for the new method are presented.
scientific article; zbMATH DE number 1406366
scientific article