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Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities

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Abstract

The typical structured variational inequalities can be interpreted as a system of equilibrium problems with a leader and two cooperative followers. Assume that, based on the instruction given by the leader, each follower can solve the individual equilibrium sub-problems in his own way. The responsibility of the leader is to give a more reasonable instruction for the next iteration loop based on the feedback information from the followers. This consideration leads us to present a parallel splitting augmented Lagrangian method (abbreviated to PSALM). The proposed method can be extended to solve the system of equilibrium problems with three separable operators. Finally, it is explained why we cannot use the same technique to develop similar methods for problems with more than three separable operators.

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  1. Department of Mathematics, Nanjing University, 22 Hankou Road, Nanjing, 210093, China

    Bing-Sheng He

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  1. Bing-Sheng He
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He, BS. Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities. Comput Optim Appl 42, 195–212 (2009). https://doi.org/10.1007/s10589-007-9109-x

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  • DOI: https://doi.org/10.1007/s10589-007-9109-x

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