Abstract
The paper concerns with novel first-order methods for monotone variational inequalities. They use a very simple linesearch procedure that takes into account a local information of the operator. Also, the methods do not require Lipschitz continuity of the operator and the linesearch procedure uses only values of the operator. Moreover, when the operator is affine our linesearch becomes very simple, namely, it needs only simple vector–vector operations. For all our methods, we establish the ergodic convergence rate. In addition, we modify one of the proposed methods for the case of a composite minimization. Preliminary results from numerical experiments are quite promising.
Original language | English |
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Pages (from-to) | 140-164 |
Number of pages | 25 |
Journal | Optimization Methods and Software |
Volume | 33 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2 Jan 2018 |
Keywords
- convex optimization
- ergodic convergence
- linesearch
- monotone operator
- nonmonotone stepsizes
- proximal methods
- variational inequality
ASJC Scopus subject areas
- Software
- Control and Optimization
- Applied Mathematics