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We give a short, self-contained proof of the interior point method and its robust version.
A new polynomial-time algorithm for linear programming
N. Karmarkar · 1984
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Matrix multiplication via arithmetic progressions
Don Coppersmith and Shmuel Winograd · 1987
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A polynomial-time algorithm, based on newton’s method, for linear programming
James Renegar · 1988
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Speeding-up linear programming using fast matrix multiplication (extended abstract)
Pravin M. Vaidya · 1989
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Interior-point polynomial algorithms in convex programming
Yurii Nesterov and Arkadii Nemirovskii · 1994
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Randomness efficient identity testing of multivariate polynomials
Adam R Klivans and Daniel Spielman · 2001
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On the riemannian geometry defined by self-concordant barriers and interior-point methods
Yurii E Nesterov, Michael J Todd, et al · 2002
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Multiplying matrices faster than coppersmith-winograd
Virginia Vassilevska Williams · 2012
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Powers of tensors and fast matrix multiplication
François Le Gall · 2014
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Path finding methods for linear programming: Solving linear programs in õ (vrank) iterations and faster algorithms for maximum flow
Yin Tat Lee and Aaron Sidford · 2014
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A faster cutting plane method and its implications for combinatorial and convex optimization
Yin Tat Lee, Aaron Sidford, and Sam Chiu-wai Wong · 2015
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Solving linear programs in the current matrix multiplication time
Michael B Cohen, Yin Tat Lee, and Zhao Song · 2018
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Improved rectangular matrix multiplication using powers of the coppersmith-winograd tensor
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Bipartite matching in nearly-linear time on moderately dense graphs
Jan van den Brand, Yin-Tat Lee, Danupon Nanongkai, Richard Peng, Thatchaphol Saranurak, Aaron Sidford, Zhao Song, and Di Wang · 2020
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Solving tall dense linear programs in nearly linear time
Jan van den Brand, Yin Tat Lee, Aaron Sidford, and Zhao Song · 2020
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A refined laser method and faster matrix multiplication
Josh Alman and Virginia Vassilevska Williams · 2021
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A nearly-linear time algorithm for linear programs with small treewidth: A multiscale representation of robust central path
Sally Dong, Yin Tat Lee, and Guanghao Ye · 2021
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Baihe Huang, Shunhua Jiang, Zhao Song, and Runzhou Tao · 2021
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