The forward–backward–forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces

•Addresses numerical algorithms for pseudo-monotone variational inequalities.•Proves the convergence of Tseng’s FBF method and validates the theoretical results with numerical experiments.•Emphasizes the interplay between discrete and continuous time approaches to variational inequalities. Tseng’s f...

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Veröffentlicht in:European journal of operational research Jg. 287; H. 1; S. 49 - 60
Hauptverfasser: Boţ, R.I., Csetnek, E.R., Vuong, P.T.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 16.11.2020
Schlagworte:
Convex programming
Dynamical system
Pseudo-monotonicity
Tseng’s FBF algorithm
Variational inequalities
Tseng’s FBF algorithm
Dynamical system
Convex programming
Pseudo-monotonicity
Variational inequalities
ISSN:0377-2217, 1872-6860
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Zusammenfassung:•Addresses numerical algorithms for pseudo-monotone variational inequalities.•Proves the convergence of Tseng’s FBF method and validates the theoretical results with numerical experiments.•Emphasizes the interplay between discrete and continuous time approaches to variational inequalities. 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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2020.04.035