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The monotone variational inequality is a central problem in mathematical programming that unifies and generalizes many important settings such as smooth convex optimization, two-player zero-sum games, convex-concave saddle point problems, etc.
Über die zerlegung definiter funktionen in quadrate
Emil Artin · 1927
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Anneaux préordonnés
Jean-Louis Krivine · 1964
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Nonlinear monotone operators and convex sets in Banach spaces
Felix E. Browder · 1965
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On some non-linear elliptic differential-functional equations
Philip Hartman and Guido Stampacchia · 1966
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Variational inequalities
Jacques-Louis Lions and Guido Stampacchia · 1967
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Méthodes d’approximation et d’itération pour les opérateurs monotones
Haïm Brezis and Moïse Sibony · 1968
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Méthodes itératives pour les équations et inéquations aux dérivées partielles non linéaires de type monotone
Moïse Sibony · 1970
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A nullstellensatz and a positivstellensatz in semialgebraic geometry
Gilbert Stengle · 1974
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The extragradient method for finding saddle points and other problems
G. M. Korpelevich · 1976
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A modification of the Arrow-Hurwicz method for search of saddle points
Leonid Denisovich Popov · 1980
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On linear convergence of iterative methods for the variational inequality problem
Paul Tseng · 1995
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Prox-method with rate of convergence O (1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems
Arkadi Nemirovski · 2004
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Interior projection-like methods for monotone variational inequalities
Alfred Auslender and Marc Teboulle · 2005
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Nicolo Cesa-Bianchi and Gabor Lugosi · 2006
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Francisco Facchinei and Jong-Shi Pang · 2007
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On accelerated proximal gradient methods for convex-concave optimization
Paul Tseng · 2008
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Aharon Ben-Tal, Laurent El Ghaoui, and Arkadi Nemirovski · 2009
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Eyal Even-Dar, Yishay Mansour, and Uri Nadav · 2009
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Halpern iteration for near-optimal and parameter-free monotone inclusion and strong solutions to variational inequalities
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