An improved proximal alternating direction method for monotone variational inequalities with separable structure

Authors:
Xiaoming Yuan
Affiliations:
Department of Mathematics, Hong Kong Baptist University, Hong Kong, China
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

To solve a class of variational inequalities with separable structure, this paper presents a new method to improve the proximal alternating direction method (PADM) in the following senses: an iterate generated by the PADM is utilized to generate a descent direction; and an appropriate step size along this descent direction is identified. Hence, a descent-like method is developed. Convergence of the new method is proved under mild assumptions. Some numerical results demonstrate that the new method is efficient.