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Banach's fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems.
On the converse of banach "fixed-point principle"
C. Bessaga · 1959
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A converse to banach’s contraction theorem
Philip R. Meyers · 1967
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How easy is local search?
David S. Johnson, Christos H. Papadimitriou, and Mihalis Yannakakis · 1988
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On the complexity of the parity argument and other inefficient proofs of existence
Christos H. Papadimitriou · 1994
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Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Aharon Ben-Tal and Arkadi Nemirovski · 2001
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Convex optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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The complexity of pure nash equilibria
Alex Fabrikant, Christos Papadimitriou, and Kunal Talwar · 2004
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On the complexity of nash equilibria and other fixed points
Kousha Etessami and Mihalis Yannakakis · 2007
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Inapproximability of pure nash equilibria
Alexander Skopalik and Berthold Vöcking · 2008
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Settling the complexity of computing two-player nash equilibria
Xi Chen, Xiaotie Deng, and Shang-Hua Teng · 2009
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The complexity of computing a nash equilibrium
Constantinos Daskalakis, Paul W Goldberg, and Christos H Papadimitriou · 2009
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Metric and topological spaces, 2010
T Körner · 2010
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Continuous local search
Constantinos Daskalakis and Christos H. Papadimitriou · 2011
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Introductory lectures on convex optimization: A basic course
Yurii Nesterov · 2013
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The contraction mapping theorem
Keith Conrad · 2014
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Understanding alternating minimization for matrix completion
Gradient descent converges to minimizers: The case of non-isolated critical points
Ioannis Panageas and Georgios Piliouras · 2016
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Can ppad hardness be based on standard cryptographic assumptions?
Alon Rosen, Gil Segev, and Ido Shahaf · 2016
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Settling the complexity of computing approximate two-player nash equilibria
Aviad Rubinstein · 2016
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Local max-cut in smoothed polynomial time
Omer Angel, Sébastien Bubeck, Yuval Peres, and Fan Wei · 2017
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Smoothed analysis of local search for the maximum-cut problem
Michael Etscheid and Heiko Röglin · 2017
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Moritz Hardt · 2014
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On the cryptographic hardness of finding a nash equilibrium
Nir Bitansky, Omer Paneth, and Alon Rosen · 2015
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Gradient descent only converges to minimizers
Jason D. Lee, Max Simchowitz, Michael I. Jordan, and Benjamin Recht · 2016
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John Fearnley, Spencer Gordon, Ruta Mehta, and Rahul Savani · 2017
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Hardness of continuous local search: Query complexity and cryptographic lower bounds
Pavel Hubacek and Eylon Yogev · 2017
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White-box vs. black-box complexity of search problems: Ramsey and graph property testing
Ilan Komargodski, Moni Naor, and Eylon Yogev · 2017
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