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We provide a condition-based analysis of two interior-point methods for unconstrained geometric programs, a class of convex programs that arise naturally in applications including matrix scaling, matrix balancing, and entropy maximization.
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Nathan Linial, Alex Samorodnitsky, and Avi Wigderson, A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents , Combinatorica 20
2000
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James Renegar, A mathematical view of interior-point methods in convex optimization , Society for Industrial and Applied Mathematics, 2001
2001
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Leonid Gurvits, Combinatorial and algorithmic aspects of hyperbolic polynomials , arXiv:math/0404474, 2004
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Arkadi Nemirovski and Levent Tunçel, “Cone-free” primal-dual path-following and potential-reduction polynomial time interior-point methods , Mathematical Programming 102
2005
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Ankit Garg, Leonid Gurvits, Rafael Oliveira, and Avi Wigderson, Algorithmic and optimization aspects of Brascamp-Lieb inequalities, via operator scaling , Geometric and Functional Analysis 28
2018
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2018
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Tsz Chiu Kwok, Lap Chi Lau, Yin Tat Lee, and Akshay Ramachandran, The Paulsen problem, continuous operator scaling, and smoothed analysis , Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (New York, NY, USA), STOC 2018, Association for Computing Machinery, 2018, pp. 182–189
2018
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Peter Bürgisser, Cole Franks, Ankit Garg, Rafael Oliveira, Michael Walter, and Avi Wigderson, Towards a theory of non-commutative optimization: Geodesic 1 1 st and 2 2 nd order methods for moment maps and polytopes , 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), 2019, pp. 845–861
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Stephen Boyd, Seung-Jean Kim, Lieven Vandenberghe, and Arash Hassibi, A tutorial on geometric programming , Optimization and Engineering 8
2007
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Peter Bürgisser and Felipe Cucker, Condition: The geometry of numerical algorithms , vol. 349, Springer Science & Business Media, 2013
2013
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Mohit Singh and Nisheeth K. Vishnoi, Entropy, optimization and counting , Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing (New York, NY, USA), STOC 2014, Association for Computing Machinery, 2014, pp. 50–59
2014
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Zeyuan Allen-Zhu, Yyuanzhi Li, Rafael Oliveira, and Avi Wigderson, Much faster algorithms for matrix scaling , 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), 2017, pp. 890–901
2017
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Michael B. Cohen, Aleksander Madry, Dimitris Tsipras, and Adrian Vladu, Matrix scaling and balancing via box constrained Newton’s method and interior point methods , 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), 2017, pp. 902–913
2017
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Zeyuan Allen-Zhu, Ankit Garg, Yuanzhi Li, Rafael Oliveira, and Avi Wigderson, Operator scaling via geodesically convex optimization, invariant theory and polynomial identity testing , Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (New York, NY, USA), STOC 2018, Association for Computing Machinery, 2018, pp. 172–181
2018
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Peter Bürgisser, Ankit Garg, Rafael Oliveira, Michael Walter, and Avi Wigderson, Alternating minimization, scaling algorithms, and the null-cone problem from invariant theory , 9th Innovations in Theoretical Computer Science Conference (ITCS 2018) (Dagstuhl, Germany) (Anna R. Karlin, ed.), Leibniz International Proceedings in Informatics (LIPIcs), vol. 94, Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2018, pp. 24:1–24:20
2018
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2019
Later among the works it cites.
2019
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Tsz Chiu Kwok, Lap Chi Lau, and Akshay Ramachandran, Spectral analysis of matrix scaling and operator scaling , 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), 2019, pp. 1184–1204
2019
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Damian Straszak and Nisheeth K. Vishnoi, Maximum entropy distributions: Bit complexity and stability , Proceedings of the Thirty-Second Conference on Learning Theory (Phoenix, USA) (Alina Beygelzimer and Daniel Hsu, eds.), PMLR, vol. 99, 2019, pp. 2861–2891
2019
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2020
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Daniel Dadush, László A. Végh, and Giacomo Zambelli, Rescaling algorithms for linear conic feasibility , Mathematics of Operations Research 45
2020
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2020
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Cole Franks and Ankur Moitra, Rigorous guarantees for Tyler’s M-estimator via quantum expansion , Proceedings of Thirty Third Conference on Learning Theory (Jacob Abernethy and Shivani Agarwal, eds.), PMLR, vol. 125, 2020, pp. 1601–1632
2020
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2020
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by same author, Operator scaling: Theory and applications , Foundations of Computational Mathematics 20
2020
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