Variational Inequalities

By Anna Nagurney. Encyclopedia of Optimization, 2009

915 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Transportation

View Paper: https://www.semanticscholar.org/paper/850a69db209b2203c674a62e04de04240b4e8b6c

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In Control and Systems Engineering

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Citations in the corpus

A Stochastic forward-backward splitting method for solving monotone inclusions in Hilbert spaces (2014, background): “The problem is to solve the following variational inequality [33, 54, 5] find w ∈ H such that (∀w ∈ H) 〈w − w | Bw〉+G(w) ≤ G(w), (5.”
Higher differentiability for solutions to a class of obstacle problems (2018, positive): “It is well known that the solution to the obstacle problem cannot be of class C2 independently of how regular the obstacle is; this led to the origin of the concept of weak solution and to the theory of variational inequalities, after the fundamental work of Lions and Stampacchia [35] (for more deta”
An adaptation of Nitscheʼs method to the Tresca friction problem (2014, background): “which admits a unique solution according to [34].”
Solving variational inequalities involving nonexpansive type mappings (2008, methodology): “The variational inequalities were initially studied by Stampachhia [10, 12] and ever since have been widely studied.”
Advances in Variational and Hemivariational Inequalities (2015, methodology): “The theory of variational inequalities and their applications represents the topics of several well-known classical monographs by Duvaut and Lions [4], Glowinski, Lions, and Trémoliéres [6], Kinderlehrer and Stampacchia [10], Baiocchi and Capelo [1], Kikuchi and Oden [9], and so on.”
Bayesian Nash equilibrium and variational inequalities (2016, background): “…of a Nash equilibrium: ∂gi ∂xi ∣∣∣∣ x=x∗ (xi − x∗i ) ≤ 0 for all xi ∈ Xi, i ∈ N. Gabay and Moulin (1980) formulated a Nash equilibrium as a solution to the above variational inequality problem, but this fact goes back to the early papers by Lions and Stampacchia (1967) and Bensoussan (1974).”
Efficient simulation of multi‐body contact problems on complex geometries: A flexible decomposition approach using constrained minimization (2009, background): “Therefore, the multi-body contact problem can be written as a variational inequality on the convex set of admissible displacements and the existence of a unique solution results from an application of well-established instruments from convex analysis, see, e. g., [9, 14, 39].”