Augmented Lagrangian theory, duality and decomposition methods for variational inequality problems (Q1411499)

The paper is devoted to extension of the augmented Lagrangian theory from convex optimization problems to constrained variational inequalities. Based on these results, the author presents a multiplier method for variational inequalities. It should be noted that similar results have been obtained by \textit{A.~Auslender and M.~Teboulle} [SIAM J. Optim., 10, No. 4, 1097--1115 (2000; Zbl 0996.49005)] and by \textit{I.V.~Konnov} [Comput. Math. Math. Phys., 41, No. 9, 1279--1291 (2001); translation from Zh. Vychisl. Mat. Mat. Fiz. 41, No. 9, 1344--1357 (2001; Zbl 1022.49008) and Optimization 51, No. 6, 907--926 (2002; Zbl 1022.49007)]. A decomposable variant of the Arrow-Hurwicz type method with the augmented Lagrangian is also presented.