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The Forward-Backward-Forward Method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces
- Publication Year :
- 2020
-
Abstract
- Tseng’s forward–backward–forward algorithm is a valuable alternative for Korpelevich’s extragradient method when solving variational inequalities over a convex and closed set governed by monotone and Lipschitz continuous operators, as it requires in every step only one projection operation. However, it is well-known that Korpelevich’s method converges and can therefore be used also for solving variational inequalities governed by pseudo-monotone and Lipschitz continuous operators. In this paper, we first associate to a pseudo-monotone variational inequality a forward–backward–forward dynamical system and carry out an asymptotic analysis for the generated trajectories. The explicit time discretization of this system results into Tseng’s forward–backward–forward algorithm with relaxation parameters, which we prove to converge also when it is applied to pseudo-monotone variational inequalities. In addition, we show that linear convergence is guaranteed under strong pseudo-monotonicity. Numerical experiments are carried out for pseudo-monotone variational inequalities over polyhedral sets and fractional programming problems.
- Subjects :
- TheoryofComputation_MISCELLANEOUS
Information Systems and Management
General Computer Science
Discretization
0211 other engineering and technologies
02 engineering and technology
Management Science and Operations Research
Industrial and Manufacturing Engineering
Projection (linear algebra)
symbols.namesake
Fractional programming
0502 economics and business
FOS: Mathematics
Applied mathematics
Mathematics - Optimization and Control
Mathematics
050210 logistics & transportation
021103 operations research
05 social sciences
Hilbert space
47J20, 90C25, 90C30, 90C52
Lipschitz continuity
Monotone polygon
Rate of convergence
Optimization and Control (math.OC)
Modeling and Simulation
Variational inequality
symbols
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....0363b5b1398d336b27caadb779884154