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\begin{thebibliography}{10}
\bibitem{barvinok1995problems}
Alexander~I. Barvinok.
\newblock Problems of distance geometry and convex properties of quadratic
maps.
\newblock {\em Discrete \& Computational Geometry}, 13(2):189--202, 1995.
\bibitem{bertsekas1976penalty}
Dimitri~P Bertsekas.
\newblock On penalty and multiplier methods for constrained minimization.
\newblock {\em SIAM Journal on Control and Optimization}, 14(2):216--235, 1976.
\bibitem{bertsekas2014constrained}
D.P. Bertsekas and W.~Rheinboldt.
\newblock {\em Constrained Optimization and Lagrange Multiplier Methods}.
\newblock Computer science and applied mathematics. Elsevier Science, 2014.
\bibitem{bhojanapalli2016dropping}
Srinadh Bhojanapalli, Anastasios Kyrillidis, and Sujay Sanghavi.
\newblock Dropping convexity for faster semi-definite optimization.
\newblock In {\em Conference on Learning Theory}, pages 530--582, 2016.
\bibitem{birgin2016evaluation}
Ernesto~G Birgin, JL~Gardenghi, Jos{\'e}~Mario Martinez, SA~Santos, and Ph~L
Toint.
\newblock Evaluation complexity for nonlinear constrained optimization using
unscaled kkt conditions and high-order models.
\newblock {\em SIAM Journal on Optimization}, 26(2):951--967, 2016.
\bibitem{bolte2017error}
J{\'e}r{\^o}me Bolte, Trong~Phong Nguyen, Juan Peypouquet, and Bruce~W Suter.
\newblock From error bounds to the complexity of first-order descent methods
for convex functions.
\newblock {\em Mathematical Programming}, 165(2):471--507, 2017.
\bibitem{bolte2014proximal}
J{\'e}r{\^o}me Bolte, Shoham Sabach, and Marc Teboulle.
\newblock Proximal alternating linearized minimization for nonconvex and
nonsmooth problems.
\newblock {\em Mathematical Programming}, 146(1-2):459--494, 2014.
\bibitem{bolte2018nonconvex}
Jerome Bolte, Shoham Sabach, and Marc Teboulle.
\newblock Nonconvex lagrangian-based optimization: monitoring schemes and
global convergence.
\newblock {\em Mathematics of Operations Research}, 2018.
\bibitem{bot2018proximal}
Radu~Ioan Bot and Dang-Khoa Nguyen.
\newblock The proximal alternating direction method of multipliers in the
nonconvex setting: convergence analysis and rates.
\newblock {\em arXiv preprint arXiv:1801.01994}, 2018.
\bibitem{boumal2016global}
Nicolas Boumal, P-A Absil, and Coralia Cartis.
\newblock Global rates of convergence for nonconvex optimization on manifolds.
\newblock {\em arXiv preprint arXiv:1605.08101}, 2016.
\bibitem{boumal2014manopt}
Nicolas Boumal, Bamdev Mishra, P-A Absil, and Rodolphe Sepulchre.
\newblock Manopt, a matlab toolbox for optimization on manifolds.
\newblock {\em The Journal of Machine Learning Research}, 15(1):1455--1459,
2014.
\bibitem{boumal2016non}
Nicolas Boumal, Vlad Voroninski, and Afonso Bandeira.
\newblock The non-convex burer-monteiro approach works on smooth semidefinite
programs.
\newblock In {\em Advances in Neural Information Processing Systems}, pages
2757--2765, 2016.
\bibitem{boyd2004convex}
S.~Boyd, S.P. Boyd, L.~Vandenberghe, and Cambridge~University Press.
\newblock {\em Convex Optimization}.
\newblock Berichte uber verteilte messysteme. Cambridge University Press, 2004.
\bibitem{Boyd2011}
Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, Jonathan Eckstein, et~al.
\newblock Distributed optimization and statistical learning via the alternating
direction method of multipliers.
\newblock {\em Foundations and Trends{\textregistered} in Machine learning},
3(1):1--122, 2011.
\bibitem{burer2003nonlinear}
Samuel Burer and Renato~DC Monteiro.
\newblock A nonlinear programming algorithm for solving semidefinite programs
via low-rank factorization.
\newblock {\em Mathematical Programming}, 95(2):329--357, 2003.
\bibitem{burer2005local}
Samuel Burer and Renato~DC Monteiro.
\newblock Local minima and convergence in low-rank semidefinite programming.
\newblock {\em Mathematical Programming}, 103(3):427--444, 2005.
\bibitem{cartis2018optimality}
Coralia Cartis, Nicholas~IM Gould, and Ph~L Toint.
\newblock Optimality of orders one to three and beyond: characterization and
evaluation complexity in constrained nonconvex optimization.
\newblock {\em Journal of Complexity}, 2018.
\bibitem{cartis2011evaluation}
Coralia Cartis, Nicholas~IM Gould, and Philippe~L Toint.
\newblock On the evaluation complexity of composite function minimization with
applications to nonconvex nonlinear programming.
\newblock {\em SIAM Journal on Optimization}, 21(4):1721--1739, 2011.
\bibitem{clason2018acceleration}
Christian Clason, Stanislav Mazurenko, and Tuomo Valkonen.
\newblock Acceleration and global convergence of a first-order primal--dual
method for nonconvex problems.
\newblock {\em arXiv preprint arXiv:1802.03347}, 2018.
\bibitem{fernandez2012local}
Damian Fernandez and Mikhail~V Solodov.
\newblock Local convergence of exact and inexact augmented lagrangian methods
under the second-order sufficient optimality condition.
\newblock {\em SIAM Journal on Optimization}, 22(2):384--407, 2012.
\bibitem{flores2012complete}
Fabi{\'a}n Flores-Baz{\'a}n, Fernando Flores-Baz{\'a}n, and Cristi{\'a}n Vera.
\newblock A complete characterization of strong duality in nonconvex
optimization with a single constraint.
\newblock {\em Journal of Global Optimization}, 53(2):185--201, 2012.
\bibitem{Gabay1976}
Daniel Gabay and Bertrand Mercier.
\newblock A dual algorithm for the solution of nonlinear variational problems
via finite element approximation.
\newblock {\em Computers \& Mathematics with Applications}, 2:17--40, 12 1976.
\bibitem{Glowinski1975}
R.~Glowinski and A.~Marroco.
\newblock Sur l'approximation, par \'el\'ements finis d'ordre un, et la
r\'esolution, par p\'enalisation-dualit\'e d'une classe de probl\`emes de
dirichlet non lin\'eaires.
\newblock {\em ESAIM: Mathematical Modelling and Numerical Analysis -
Mod\'elisation Math\'ematique et Analyse Num\'erique}, 9(R2):41--76, 1975.
\bibitem{gomez2019fast}
Fabian~Latorre G{\'o}mez, Armin Eftekhari, and Volkan Cevher.
\newblock Fast and provable admm for learning with generative priors.
\newblock {\em arXiv preprint arXiv:1907.03343}, 2019.
\bibitem{guo2017convergence}
Ke~Guo, DR~Han, and Ting-Ting Wu.
\newblock Convergence of alternating direction method for minimizing sum of two
nonconvex functions with linear constraints.
\newblock {\em International Journal of Computer Mathematics},
94(8):1653--1669, 2017.
\bibitem{hong2016convergence}
Mingyi Hong, Zhi-Quan Luo, and Meisam Razaviyayn.
\newblock Convergence analysis of alternating direction method of multipliers
for a family of nonconvex problems.
\newblock {\em SIAM Journal on Optimization}, 26(1):337--364, 2016.
\bibitem{jiang2019structured}
Bo~Jiang, Tianyi Lin, Shiqian Ma, and Shuzhong Zhang.
\newblock Structured nonconvex and nonsmooth optimization: algorithms and
iteration complexity analysis.
\newblock {\em Computational Optimization and Applications}, 72(1):115--157,
2019.
\bibitem{karimi2016linear}
Hamed Karimi, Julie Nutini, and Mark Schmidt.
\newblock Linear convergence of gradient and proximal-gradient methods under
the polyak-{\l}ojasiewicz condition.
\newblock In {\em Joint European Conference on Machine Learning and Knowledge
Discovery in Databases}, pages 795--811. Springer, 2016.
\bibitem{khot2011grothendieck}
Subhash Khot and Assaf Naor.
\newblock Grothendieck-type inequalities in combinatorial optimization.
\newblock {\em arXiv preprint arXiv:1108.2464}, 2011.
\bibitem{li2015global}
Guoyin Li and Ting~Kei Pong.
\newblock Global convergence of splitting methods for nonconvex composite
optimization.
\newblock {\em SIAM Journal on Optimization}, 25(4):2434--2460, 2015.
\bibitem{liu2019linearized}
Qinghua Liu, Xinyue Shen, and Yuantao Gu.
\newblock Linearized admm for nonconvex nonsmooth optimization with convergence
analysis.
\newblock {\em IEEE Access}, 2019.
\bibitem{lovasz2003semidefinite}
L{\'a}szl{\'o} Lov{\'a}sz.
\newblock Semidefinite programs and combinatorial optimization.
\newblock In {\em Recent advances in algorithms and combinatorics}, pages
137--194. Springer, 2003.
\bibitem{moreau1962decomposition}
Jean~Jacques Moreau.
\newblock Decomposition orthogonale d'un espace hilbertien selon deux cones
mutuellement polaires.
\newblock 1962.
\bibitem{mossel2015consistency}
Elchanan Mossel, Joe Neeman, and Allan Sly.
\newblock Consistency thresholds for the planted bisection model.
\newblock In {\em Proceedings of the forty-seventh annual ACM symposium on
Theory of computing}, pages 69--75. ACM, 2015.
\bibitem{parikh2014proximal}
Neal Parikh, Stephen Boyd, et~al.
\newblock Proximal algorithms.
\newblock {\em Foundations and Trends in Optimization}, 1(3):127--239, 2014.
\bibitem{park2016provable}
Dohyung Park, Anastasios Kyrillidis, Srinadh Bhojanapalli, Constantine
Caramanis, and Sujay Sanghavi.
\newblock Provable burer-monteiro factorization for a class of norm-constrained
matrix problems.
\newblock {\em arXiv preprint arXiv:1606.01316}, 2016.
\bibitem{pataki1998rank}
G{\'a}bor Pataki.
\newblock On the rank of extreme matrices in semidefinite programs and the
multiplicity of optimal eigenvalues.
\newblock {\em Mathematics of operations research}, 23(2):339--358, 1998.
\bibitem{raghavendra2008optimal}
Prasad Raghavendra.
\newblock Optimal algorithms and inapproximability results for every csp?
\newblock In {\em Proceedings of the fortieth annual ACM symposium on Theory of
computing}, pages 245--254. ACM, 2008.
\bibitem{rockafellar1993lagrange}
R~Tyrrell Rockafellar.
\newblock Lagrange multipliers and optimality.
\newblock {\em SIAM review}, 35(2):183--238, 1993.
\bibitem{rockafellar2015convex}
R.T. Rockafellar.
\newblock {\em Convex Analysis}.
\newblock Princeton Landmarks in Mathematics and Physics. Princeton University
Press, 2015.
\bibitem{sahin2019inexact}
Mehmet~Fatih Sahin, Armin Eftekhari, Ahmet Alacaoglu, Fabian Latorre, and
Volkan Cevher.
\newblock An inexact augmented lagrangian framework for nonconvex optimization
with nonlinear constraints.
\newblock {\em arXiv preprint arXiv:1906.11357}, 2019.
\bibitem{singer2011angular}
Amit Singer.
\newblock Angular synchronization by eigenvectors and semidefinite programming.
\newblock {\em Applied and computational harmonic analysis}, 30(1):20, 2011.
\bibitem{singer2011three}
Amit Singer and Yoel Shkolnisky.
\newblock Three-dimensional structure determination from common lines in
cryo-em by eigenvectors and semidefinite programming.
\newblock {\em SIAM journal on imaging sciences}, 4(2):543--572, 2011.
\bibitem{song2007dependence}
Le~Song, Alex Smola, Arthur Gretton, and Karsten~M Borgwardt.
\newblock A dependence maximization view of clustering.
\newblock In {\em Proceedings of the 24th international conference on Machine
learning}, pages 815--822. ACM, 2007.
\bibitem{waldspurger2018rank}
Ir{\`e}ne Waldspurger and Alden Waters.
\newblock Rank optimality for the burer-monteiro factorization.
\newblock {\em arXiv preprint arXiv:1812.03046}, 2018.
\bibitem{wang2018convergence}
Fenghui Wang, Wenfei Cao, and Zongben Xu.
\newblock Convergence of multi-block bregman admm for nonconvex composite
problems.
\newblock {\em Science China Information Sciences}, 61(12):122101, 2018.
\bibitem{wang2015global}
Yu~Wang, Wotao Yin, and Jinshan Zeng.
\newblock Global convergence of admm in nonconvex nonsmooth optimization.
\newblock {\em arXiv preprint arXiv:1511.06324}, 2015.
\bibitem{xu2017accelerated}
Yangyang Xu.
\newblock Accelerated first-order primal-dual proximal methods for linearly
constrained composite convex programming.
\newblock {\em SIAM Journal on Optimization}, 27(3):1459--1484, 2017.
\bibitem{xu2017globally}
Yangyang Xu and Wotao Yin.
\newblock A globally convergent algorithm for nonconvex optimization based on
block coordinate update.
\newblock {\em Journal of Scientific Computing}, 72(2):700--734, 2017.
\bibitem{yang2017alternating}
Lei Yang, Ting~Kei Pong, and Xiaojun Chen.
\newblock Alternating direction method of multipliers for a class of nonconvex
and nonsmooth problems with applications to background/foreground extraction.
\newblock {\em SIAM Journal on Imaging Sciences}, 10(1):74--110, 2017.
\bibitem{yurtsever2018conditional}
Alp Yurtsever, Olivier Fercoq, Francesco Locatello, and Volkan Cevher.
\newblock A conditional gradient framework for composite convex minimization
with applications to semidefinite programming.
\newblock {\em arXiv preprint arXiv:1804.08544}, 2018.
\bibitem{zhao1998semidefinite}
Qing Zhao, Stefan~E Karisch, Franz Rendl, and Henry Wolkowicz.
\newblock Semidefinite programming relaxations for the quadratic assignment
problem.
\newblock {\em Journal of Combinatorial Optimization}, 2(1):71--109, 1998.
\end{thebibliography}

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