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We present a faster interior-point method for optimizing sum-of-squares (SOS) polynomials, which are a central tool in polynomial optimization and capture convex programming in the Lasserre hierarchy.
A new polynomial-time algorithm for linear programming
Narendra Karmarkar · 1984
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Karmarkar’s algorithm and its place in applied mathematics
Gilbert Strang · 1987
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Speeding-up linear programming using fast matrix multiplication
Pravin M Vaidya · 1989
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Interior-point polynomial algorithms in convex programming
Y. Nesterov and A. Nemirovskii · 1994
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An o n L o\sqrt{nL} -iteration homogeneous and self-dual linear programming algorithm
Yinyu Ye, Michael J Todd, and Shinji Mizuno · 1994
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Positive polynomials on semi-algebraic sets
Mihai Putinar and Florian-Horia Vasilescu · 1999
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Yuri Nesterov · 2000
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Structured Matrices and Polynomials
Victor Y. Pan · 2001
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A Mathematical View of Interior-Point Methods in Convex Optimization
James Renegar · 2001
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On the complexity of fixed parameter clique and dominating set
Friedrich Eisenbrand and Fabrizio Grandoni · 2004
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New upper bounds for kissing numbers from semidefinite programming
Christine Bachoc and Frank Vallentin · 2006
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Multidimensional FIR filter design via trigonometric sum-of-squares optimization
Tae Roh, Bogdan Dumitrescu, and Lieven Vandenberghe · 2007
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Experimental study of energy-minimizing point configurations on spheres
Brandon Ballinger, Grigoriy Blekherman, Henry Cohn, Noah Giansiracusa, Elizabeth Kelly, and Achill Schürmann · 2009
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Sums of squares, moment matrices and optimization over polynomials
M. Laurent · 2009
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Computing approximate fekete points by qr factorizations of vandermonde matrices
Alvise Sommariva and Marco Vianello · 2009
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Computing multivariate fekete and leja points by numerical linear algebra
L. Bos, S. De Marchi, A. Sommariva, and M. Vianello · 2010
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Rounding semidefinite programming hierarchies via global correlation, 2011
Boaz Barak, Prasad Raghavendra, and David Steurer · 2011
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Semidefinite optimization and convex algebraic geometry
Grigoriy Blekherman, Pablo A Parrilo, and Rekha R Thomas · 2012
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Optimal designs for rational function regression
Dávid Papp · 2012
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The power of sum-of-squares for detecting hidden structures
Samuel B. Hopkins, Pravesh K. Kothari, Aaron Potechin, Prasad Raghavendra, Tselil Schramm, and David Steurer · 2017
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Improved rectangular matrix multiplication using powers of the coppersmith-winograd tensor
François Le Gall and Florent Urrutia · 2018
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Mixture models, robustness, and sum of squares proofs
Samuel B. Hopkins and Jerry Li · 2018
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A nearly tight sum-of-squares lower bound for the planted clique problem
Boaz Barak, Samuel B. Hopkins, Jonathan A. Kelner, Pravesh K. Kothari, Ankur Moitra, and Aaron Potechin · 2019
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Solving linear programs in the current matrix multiplication time
Michael B Cohen, Yin Tat Lee, and Zhao Song · 2019
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Solving linear programs with sqrt(rank) linear system solves
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Fast matrix multiplication
Markus Bläser · 2013
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François Le Gall · 2014
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An Introduction to Polynomial and Semi-Algebraic Optimization
Jean Bernard Lasserre · 2015
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On the Power of Lasserre SDP Hierarchy
Ning Tan · 2015
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Optimal power flow as a polynomial optimization problem
Bissan Ghaddar, Jakub Marecek, and M. Mevissen · 2016
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Semidefinite approximations of the polynomial abscissa
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Yin Tat Lee, Zhao Song, and Qiuyi Zhang · 2019
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Sum-of-squares optimization without semidefinite programming
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A faster interior point method for semidefinite programming, 2020
Haotian Jiang, Tarun Kathuria, Yin Tat Lee, Swati Padmanabhan, and Zhao Song · 2020
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Sum of squares : theory and applications : AMS short course, sum of squares : theory and applications, January 14-15, 2019, Baltimore, Maryland
Pablo Parrilo · 2020
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A refined laser method and faster matrix multiplication
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