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2014

Accelerated Schemes For A Class of Variational Inequalities

Chen, Yunmei, Lan, Guanghui, Ouyang, Yuyuan

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We propose a novel method, namely the accelerated mirror-prox (AMP) method, for computing the weak solutions of a class of deterministic and stochastic monotone variational inequalities (VI).

The main idea of this algorithm is to incorporate a multi-step acceleration scheme into the mirror-prox method.
For both deterministic and stochastic VIs, the developed AMP method computes the weak solutions with optimal rate of convergence.
In particular, if the monotone operator in VI consists of the gradient of a smooth function, the rate of convergence of the AMP method can be accelerated in terms of its dependence on the Lipschitz constant of the smooth function.

Accelerated Schemes For A Class of Variational Inequalities · Around

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1967
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R. T. Rockafellar
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in Russian; English translation in Matekon
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A. Nemirovski and D. Yudin
1983
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translated as Soviet Math. Docl
Y. Nesterov · 1983
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A. S. Nemirovski
1992
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