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We present algorithmic applications of an approximate version of Carath\'{e}odory's theorem.
Two-person nonzero-sum games and quadratic programming
Olvi L. Mangasarian and H. Stone · 1964
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Maxima for graphs and a new proof of a theorem of Turán
T. S. Motzkin and E. G. Straus · 1965
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A generalization of Radon’s theorem
Helge Tverberg · 1966
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Classical Banach spaces
Joram Lindenstrauss and Lior Tzafriri · 1973
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The moduli of smoothness and convexity and the Rademacher averages of the trace classes S p ( 1 ≤ p < ∞ ) S_{p}\ (1\leq p<\infty)
Nicole Tomczak-Jaegermann · 1974
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Remarques sur un résultat non publié de B. Maurey (French) [Remarks on an unpublished result of B. Maurey]
Gilles Pisier · 1981
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A generalization of carathéodory’s theorem
Imre Bárány · 1982
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Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces
Bernd Carl · 1985
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On the duality problem for entropy numbers of operators
Jean Bourgain, Alain Pajor, SJ Szarek, and N Tomczak-Jaegermann · 1989
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A course in convexity
Alexander Barvinok · 2002
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Lectures on discrete geometry
Jiří Matoušek · 2002
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Playing large games using simple strategies
Richard J Lipton, Evangelos Markakis, and Aranyak Mehta · 2003
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Sparse games are hard
Xi Chen, Xiaotie Deng, and Shang-Hua Teng · 2006
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A note on approximate Nash equilibria
Constantinos Daskalakis, Aranyak Mehta, and Christos Papadimitriou · 2006
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Polynomial algorithms for approximating Nash equilibria of bimatrix games
Spyros C Kontogiannis, Panagiota N Panagopoulou, and Paul G Spirakis · 2006
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New algorithms for approximate Nash equilibria in bimatrix games
Hartwig Bosse, Jaroslaw Byrka, and Evangelos Markakis · 2007
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Progress in approximate Nash equilibria
Constantinos Daskalakis, Aranyak Mehta, and Christos Papadimitriou · 2007
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Approximating Nash equilibria using small-support strategies
Tomas Feder, Hamid Nazerzadeh, and Amin Saberi · 2007
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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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On oblivious ptas’s for Nash equilibrium
Constantinos Daskalakis and Christos H Papadimitriou · 2009
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Detecting high log-densities: an O ( n 1 / 4 ) O(n^{1/4}) approximation for densest k-subgraph
Aditya Bhaskara, Moses Charikar, Eden Chlamtac, Uriel Feige, and Aravindan Vijayaraghavan · 2010
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Practical and efficient approximations of Nash equilibria for win-lose games based on graph spectra
Haralampos Tsaknakis and Paul G Spirakis · 2010
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Inapproximability of densest κ \kappa -subgraph from average case hardness
Noga Alon, Sanjeev Arora, Rajsekar Manokaran, Dana Moshkovitz, and Omri Weinstein · 2011
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How hard is it to approximate the best Nash equilibrium?
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Inequalities: a journey into linear analysis
D.J.H. Garling · 2007
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Games of fixed rank: A hierarchy of bimatrix games
Ravi Kannan and Thorsten Theobald · 2007
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Efficient algorithms for constant well supported approximate equilibria in bimatrix games
Spyros C Kontogiannis and Paul G Spirakis · 2007
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Algorithmic game theory
Noam Nisan, Tim Roughgarden, Eva Tardos, and Vijay V Vazirani · 2007
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An optimization approach for approximate Nash equilibria
Haralampos Tsaknakis and Paul G Spirakis · 2007
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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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Elad Hazan and Robert Krauthgamer · 2011
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Moment inequalities for sums of random matrices and their applications in optimization
Anthony Man-Cho So · 2011
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The approximate rank of a matrix and its algorithmic applications: approximate rank
Noga Alon, Troy Lee, Adi Shraibman, and Santosh Vempala · 2013
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On the complexity of approximating a Nash equilibrium
Constantinos Daskalakis · 2013
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The cover number of a matrix and its algorithmic applications
Noga Alon, Troy Lee, and Adi Shraibman · 2014
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Approximating the best Nash equilibrium in n o ( log n ) n^{o(\log n)} -time breaks the exponential time hypothesis
Mark Braverman, Young Kun Ko, and Omri Weinstein · 2015
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