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This paper studies first order methods for solving smooth minimax optimization problems $\min_x \max_y g(x,y)$ where $g(\cdot,\cdot)$ is smooth and $g(x,\cdot)$ is concave for each $x$.
“On general minimax theorems.”
Maurice Sion · 1958
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“On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space”
Ronald Bruck · 1977
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“An introduction to variational inequalities and their applications”
David Kinderlehrer and Guido Stampacchia · 1980
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“Efficient methods for solving variational inequalities”
Arkadi Nemirovski · 1981
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“A method for solving the convex programming problem with convergence rate O ( 1 / k 2 ) O(1/k^{2}) ”
Yurii Nesterov · 1983
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“Elementary proof for Sion’s minimax theorem”
Hidetoshi Komiya · 1988
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“Introductory lectures on convex programming volume i: Basic course”, 1998
Yurii Nesterov · 1998
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A Kruger · 2003
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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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Yu Nesterov · 2005
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Dimitri Bertsekas · 2009
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Sham Kakade, Shai Shalev-Shwartz and Ambuj Tewari · 2009
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