Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities

By Bingsheng He, L. Liao. 2002

255 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/af11c4bc013be2e1c87237a70e677234fe10c93e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

On solving contact problems with Coulomb friction: formulations and numerical comparisons (2018, methodology): “In (He and Liao, 2002) and in the context of prediction– correction, the authors propose to use the rule ρk = ρk−1ν and if the criteria (100) is largely satisfied for ρk, the value is increased.”
Transit assignment: Approach-based formulation, extragradient method, and paradox (2014, methodology): “The extragradient method with adaptive stepsizes was first developed by He and Liao (2002), and has been shown to converge under the condition that the mapping function is pseudomonotone, which is a mild condition compared to the monotone requirement (Schaible, 1995).”
Multi-task feature selection (2006, background): “Solving each of these problems independently is equivalent1 to solving the global 1Provided the regularization coefficient λ is the same across tasks. problem obtained by summing the objectives: min W L∑ l=1 1 Nl Nl∑ i=1 J l(wl, xli, y l i) + λ L∑ l=1 ‖wl‖1 (1) where W = (wlk)l,k is the matrix with…”
Structured Prediction, Dual Extragradient and Bregman Projections (2006, methodology): “This usually leads to oscillations, and indeed, this method is generally not guaranteed to converge for bilinear objectives for any step size (Korpelevich, 1976; He and Liao, 2002).”
Some developments in general variational inequalities (2004, background): “He and Liao [43] and Sun [132,133] used d1ðuÞ, defined by (4.”
An approximate proximal-extragradient type method for monotone variational inequalities (2004, methodology): “Since th problems are solved approximately by the iterative method in [7], the number of total”
A Discriminative Matching Approach to Word Alignment (2005, methodology): “The method is guaranteed to converge linearly to a solution w∗, z∗ (Korpelevich, 1976; He and Liao, 2002; Taskar et al., 2005b).”
Structured Prediction via the Extragradient Method (2005, methodology): “Under mild conditions, the m ethod is guaranteed to converge linearly to a solution w, z [14, 11].”
Extragradient Methods for Pseudomonotone Variational Inequalities (2003, methodology): “Since K is a closed convex set, using ( 6 ) we have”