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We consider MaxCut-type semidefinite programs (SDP) which admit a low rank solution.
Self-entrainment of a population of coupled non-linear oscillators
Y. Kuramoto · 1975
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Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
M. X. Goemans and D. P. Williamson · 1995
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On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues
G. Pataki · 1998
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Solving large-scale sparse semidefinite programs for combinatorial optimization
S. J. Benson, Y. Ye, and X. Zhang · 2000
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A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
S. Burer and R. D. C. Monteiro · 2003
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Learning the kernel matrix with semidefinite programming
G. R. G. Lanckriet, N. Cristianini, P. Bartlett, L. El Ghaoui, and M. I. Jordan · 2004
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Optimization algorithms on matrix manifolds
P.-A. Absil · 2008
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Low-rank optimization on the cone of positive semidefinite matrices
M. Journée, F. Bach, P.-A. Absil, and R. Sepulchre · 2010
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PhaseLift: exact and stable signal recovery from magnitude measurements via convex programming
E. J. Candès, T. Strohmer, and V. Voroninski · 2013
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Decoding binary node labels from censored edge measurements: Phase transition and efficient recovery
E. Abbe, A. S. Bandeira, A. Bracher, and A. Singer · 2014
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Phase recovery, maxcut and complex semidefinite programming
I. Waldspurger, A. d’Aspremont, and S. Mallat · 2015
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Conic optimization via operator splitting and homogeneous self-dual embedding
B. O’donoghue, E. Chu, N. Parikh, and S. Boyd · 2016
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Solving SDPs for synchronization and MaxCut problems via the Grothendieck inequality
S. Mei, T. Misiakiewicz, A. Montanari, and R. I. Oliveira · 2017
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Random Laplacian matrices and convex relaxations
A. S. Bandeira · 2018
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High-dimensional probability: An introduction with applications in data science , volume 47
R. Vershynin · 2018
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First-order methods almost always avoid strict saddle points
J. D. Lee, I. Panageas, G. Piliouras, M. Simchowitz, M. I. Jordan, and B. Recht · 2019
Expander graphs are globally synchronizing
P. Abdalla, A. S. Bandeira, M. Kassabov, V. Souza, S. H. Strogatz, and A. Townsend · 2022
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The Burer-Monteiro SDP method can fail even above the Barvinok-Pataki bound
L. O’Carroll, V. Srinivas, and A. Vijayaraghavan · 2022
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An introduction to optimization on smooth manifolds
N. Boumal · 2023
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Benign landscapes of low-dimensional relaxations for orthogonal synchronization on general graphs
A. D. McRae and N. Boumal · 2024
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A. D. McRae, P. Abdalla, A. S. Bandeira, and N. Boumal · 2024
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On the landscape of synchronization networks: A perspective from nonconvex optimization
S. Ling, R. Xu, and A. S. Bandeira · 2019
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Deterministic guarantees for Burer-Monteiro factorizations of smooth semidefinite programs
N. Boumal, V. Voroninski, and A. S. Bandeira · 2020
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Rank optimality for the Burer-Monteiro factorization
I. Waldspurger and A. Waters · 2020
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Improved global guarantees for the nonconvex Burer–Monteiro factorization via rank overparameterization
R. Y. Zhang · 2024
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The random graph process is globally synchronizing
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Local geometry determines global landscape in low-rank factorization for synchronization
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Benign landscapes for synchronization on spheres via normalized Laplacian matrices
A. D. McRae · 2025
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