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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China

    Xiaoming Yuan

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  1. Xiaoming Yuan
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Correspondence to Xiaoming Yuan.

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This author was supported in part by the RGC Grant 203009 and the NSFC grant 10701055.

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Yuan, X. An improved proximal alternating direction method for monotone variational inequalities with separable structure. Comput Optim Appl 49, 17–29 (2011). https://doi.org/10.1007/s10589-009-9293-y

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  • DOI: https://doi.org/10.1007/s10589-009-9293-y

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