Abstract
In the literature, it was shown recently that the Douglas-Rachford alternating direction method of multipliers can be combined with the logarithmic-quadratic proximal regularization for solving a class of variational inequalities with separable structures. This paper studies the inexact version of this combination, where the resulting subproblems are allowed to be solved approximately subject to different inexactness criteria. We prove the global convergence and establish worst-case convergence rates for the derived inexact algorithms.
Original language | English |
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Pages (from-to) | 412-436 |
Number of pages | 25 |
Journal | Journal of Optimization Theory and Applications |
Volume | 159 |
Issue number | 2 |
DOIs | |
Publication status | Published - Nov 2013 |
Scopus Subject Areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics
User-Defined Keywords
- Alternating direction method of multipliers
- Convergence rate
- Inexact
- Logarithmic-quadratic proximal regularization
- Variational inequality