一种求解单调变分不等式的部分并行分裂LQP交替方向法

doi:10.15960/j.cnki.issn.1007-6093.2020.01.008

Abstract

Abstract: Logarithmic-quadratic proximal (LQP) alternating direction method of multipliers is a very effective method for solving monotone variational inequality with separable structure. It can make full use of the objective function of the separable structure, the original problem is decomposed into multiple sub-problems which is easier to be solved. Logarithmic-quadratic proximal (LQP) alternating direction method of multipliers are also suitable ones for solving large-scale problem. For monotone variational inequality problem with three separable operators, combining the augmented Lagrangian method with the LQP alternating direction method of multipliers, a partial parallel splitting LQP alternating direction method of multipliers is obtained. We construct two descent directions, the new direction is obtained by combined with the two descent directions, and an appropriate step size is derived along this new descent direction. And we prove the global convergence of the algorithm under a weaker assumption.

Key words: variational inequality, parallel splitting method, logarithmic-quadratic proximal method, alternating direction method of multipliers

CLC Number:

O221.2

LI Chaoqiong, LI Feng. A partial parallel splitting LQP alternating direction method of multipliers for solving monotone variational inequalities[J]. Operations Research Transactions, 2020, 24(1): 101-114.

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A partial parallel splitting LQP alternating direction method of multipliers for solving monotone variational inequalities

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