Modification of the extra-gradient method for solving variational inequalities and certain optimization problems

By E. Khobotov. 1989

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In Optimization & Training

Citations in the corpus

Painless Stochastic Gradient: Interpolation, Line-Search, and Convergence Rates (2019, methodology): “We now describe a “Lipschitz” line-search strategy [39, 33, 32] in order to automatically set the step-size for SEG.”
The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space (2011, background): “, [3,4,5] and references therein, to name but a few.”
Structured Prediction via the Extragradient Method (2005, methodology): “This method is generally not guaranteed to con verge for bilinear objectives [14, 13, 11].”
Unified Framework of Extragradient-Type Methods for Pseudomonotone Variational Inequalities (2001, background): “Combining the inequalities ( 8 )–(10), and using the fact that the projection of any vector onto a closed convex set is unique, we obtain the desired result.”
Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence (2020, background): “Several applications of VI(A,C) (1) are discussed in [2, 4, 18, 25, 26, 27, 32].”
On solving contact problems with Coulomb friction: formulations and numerical comparisons (2018, methodology): “In the original article of (Khobotov, 1987), there is no procedure to size ρ̄ or to update it.”
Proximal Reinforcement Learning: A New Theory of Sequential Decision Making in Primal-Dual Spaces (2014, methodology): “Khobotov [138] proved that the extragradient method converges under the weaker requirement of pseudo-monotone mappings, 6 when the learning rate is automatically adjusted based on a local measure of the Lipschitz constant.”
Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space (2011, background): “, [16, 17, 23] and references therein, to name but a few.”