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Historically, scalability has been a major challenge to the successful application of semidefinite programming in fields such as machine learning, control, and robotics.
Sieve-SDP: a simple facial reduction algorithm to preprocess semidefinite programs
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Uber die Abgrenzung der Eigenwerte einer Matrix
S. A. Gershgorin · 1931
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Augmented Lagrangians and applications of the proximal point algorithm in convex programming
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L. Lovász · 1979
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R. Grone, C. R. Johnson, E. M. Sá, and H. Wolkowicz · 1984
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Positive semidefinite matrices with a given sparsity pattern
J. Agler, W. Helton, S. McCullough, and L. Rodman · 1988
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D. C. Liu and J. Nocedal · 1989
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Positive polynomials on compact semi-algebraic sets
M. Putinar · 1993
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Problems of distance geometry and convex properties of quadratic maps
A. I. Barvinok · 1995
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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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L. Vandenberghe and S. Boyd · 1996
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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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Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
P. A. Parrilo · 2000
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Exploiting sparsity in semidefinite programming via matrix completion I: General framework
M. Fukuda, M. Kojima, K. Murota, and K. Nakata · 2001
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Global optimization with polynomials and the problem of moments
J. B. Lasserre · 2001
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SeDuMi version 1.05 , Oct. 2001
J. Sturm · 2001
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SOSTOOLS: Sum of squares optimization toolbox for MATLAB , 2002-05
S. Prajna, A. Papachristodoulou, and P. A. Parrilo · 2002
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Semidefinite programming in the space of partial positive semidefinite matrices
S. Burer · 2003
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A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
S. Burer and R. D. Monteiro · 2003
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Semidefinite programming relaxations for semialgebraic problems
P. A. Parrilo · 2003
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Symmetry groups, semidefinite programs, and sums of squares
K. Gatermann and P. A. Parrilo · 2004
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Yalmip: a toolbox for modeling and optimization in matlab
J. Löfberg · 2004
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Fast algorithms for approximate semidefinite programming using the multiplicative weights update method
S. Arora, E. Hazan, and S. Kale · 2005
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Local minima and convergence in low-rank semidefinite programming
S. Burer and R. D. Monteiro · 2005
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Positive polynomials in control , volume 312
D. Henrion and A. Garulli · 2005
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Probabilistic Robotics
S. Thrun, W. Burgard, and D. Fox · 2005
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DSDP5 user guide-software for semidefinite programming
S. J. Benson, Y. Ye, et al · 2006
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Trust-region methods on Riemannian manifolds
P.-A. Absil, C. G. Baker, and K. A. Gallivan · 2007
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The Netflix prize
J. Bennett, S. Lanning, et al · 2007
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A direct formulation for sparse PCA using semidefinite programming
A. d Aspremont, L. E. Ghaoui, M. I. Jordan, and G. R. Lanckriet · 2007
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Fast low-rank semidefinite programming for embedding and clustering
B. Kulis, A. C. Surendran, and J. C. Platt · 2007
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Approximating k-means-type clustering via semidefinite programming
J. Peng and Y. Wei · 2007
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Structured semidefinite programs for the control of symmetric systems
R. Cogill, S. Lall, and P. A. Parrilo · 2008
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Sparse approximate solutions to semidefinite programs
E. Hazan · 2008
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Optimization Algorithms on Matrix Manifolds
P.-A. Absil, R. Mahony, and R. Sepulchre · 2009
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User’s manual for SparseCoLO: conversion methods for sparse conic-form linear optimization problems
K. Fujisawa, S. Kim, M. Kojima, Y. Okamoto, and M. Yamashita · 2009
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Symmetry in semidefinite programs
F. Vallentin · 2009
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Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones
M. S. Andersen, J. Dahl, and L. Vandenberghe · 2010
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Matrix completion with noise
E. J. Candès and Y. Plan · 2010
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Exploiting special structure in semidefinite programming: a survey of theory and applications
E. De Klerk · 2010
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Copositive programming–a survey
M. Dür · 2010
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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
Cited alongside, same era.
Explicit sensor network localization using semidefinite representations and facial reductions
N. Krislock and H. Wolkowicz · 2010
Cited alongside, same era.
Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
B. Recht, M. Fazel, and P. A. Parrilo · 2010
Cited alongside, same era.
Pymanopt: A python toolbox for optimization on manifolds using automatic differentiation
J. Townsend, N. Koep, and S. Weichwald · 2016
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Reduction of SDPs in H-infinity control of SISO systems and performance limitations analysis
H. Waki, Y. Ebihara, and N. Sebe · 2016
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Sum of squares basis pursuit with linear and second order cone programming
A. A. Ahmadi and G. Hall · 2017
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Optimization over structured subsets of positive semidefinite matrices via column generation
A. A. Ahmadi, S. Dash, and G. Hall · 2017
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The many faces of degeneracy in conic optimization
D. Drusvyatskiy, H. Wolkowicz, et al · 2017
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A Newton-CG augmented Lagrangian method for semidefinite programming
X.-Y. Zhao, D. Sun, and K.-C. Toh · 2010
Cited alongside, same era.
RTRMC: A Riemannian trust-region method for low-rank matrix completion
N. Boumal and P.-a. Absil · 2011
Cited alongside, same era.
Distributed optimization and statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein · 2011
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Robust principal component analysis?
E. J. Candès, X. Li, Y. Ma, and J. Wright · 2011
Cited alongside, same era.
Projection methods for conic feasibility problems: applications to polynomial sum-of-squares decompositions
D. D. Henrion and J. Malick · 2011
Cited alongside, same era.
Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion
S. Kim, M. Kojima, M. Mevissen, and M. Yamashita · 2011
Cited alongside, same era.
I. Dunning, J. Huchette, and M. Lubin · 2017
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An extended Frank–Wolfe method with “in-face” directions, and its application to low-rank matrix completion
R. M. Freund, P. Grigas, and R. Mazumder · 2017
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A bounded degree SOS hierarchy for polynomial optimization
J. B. Lasserre, K.-C. Toh, and S. Yang · 2017
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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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Universal adversarial perturbations
S.-M. Moosavi-Dezfooli, A. Fawzi, O. Fawzi, and P. Frossard · 2017
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SCS: Splitting conic solver, version 2.1.0
B. O’Donoghue, E. Chu, N. Parikh, and S. Boyd · 2017
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Reduction methods in semidefinite and conic optimization
F. N. Permenter · 2017
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Evaluating robustness of neural networks with mixed integer programming
V. Tjeng, K. Xiao, and R. Tedrake · 2017
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The mixing method: coordinate descent for low-rank semidefinite programming
P.-W. Wang, W.-C. Chang, and J. Z. Kolter · 2017
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Provable defenses against adversarial examples via the convex outer adversarial polytope
E. Wong and J. Z. Kolter · 2017
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Sketchy decisions: Convex low-rank matrix optimization with optimal storage
A. Yurtsever, M. Udell, J. A. Tropp, and V. Cevher · 2017
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Scalable design of structured controllers using chordal decomposition
Y. Zheng, R. P. Mason, and A. Papachristodoulou · 2017
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URL https://docs.mosek.com/8.1/intro/index.html
Introducing the MOSEK Optimization Suite , 2018 · 2018
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Convergence rate of block-coordinate maximization Burer-Monteiro method for solving large SDPs
M. A. Erdogdu, A. Ozdaglar, P. A. Parrilo, and N. D. Vanli · 2018
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Optimization over nonnegative and convex polynomials with and without semidefinite programming
G. Hall · 2018
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A two-step pre-processing for semidefinite programming
V. Kungurtsev and J. Marecek · 2018
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J. G. Mangelson, J. Liu, R. M. Eustice, and R. Vasudevan · 2018
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Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone
F. Permenter and P. Parrilo · 2018
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The PICOS Documentation , 2018
PICOS · 2018
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Semidefinite relaxations for certifying robustness to adversarial examples
A. Raghunathan, J. Steinhardt, and P. S. Liang · 2018
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A geometric analysis of phase retrieval
J. Sun, Q. Qu, and J. Wright · 2018
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Efficient formal safety analysis of neural networks
S. Wang, K. Pei, J. Whitehouse, J. Yang, and S. Jana · 2018
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Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity
T. Weisser, J. B. Lasserre, and K.-C. Toh · 2018
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Verification for machine learning, autonomy, and neural networks survey
W. Xiang, P. Musau, A. A. Wild, D. M. Lopez, N. Hamilton, X. Yang, J. Rosenfeld, and T. T. Johnson · 2018
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A. A. Ahmadi and G. Hall · 2019
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DSOS and SDSOS optimization: more tractable alternatives to sum of squares and semidefinite optimization
A. A. Ahmadi and A. Majumdar · 2019
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An optimal-storage approach to semidefinite programming using approximate complementarity
L. Ding, A. Yurtsever, V. Cevher, J. A. Tropp, and M. Udell · 2019
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M. Fazlyab, M. Morari, and G. J. Pappas · 2019
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Engineering and business applications of sum of squares polynomials
G. Hall · 2019
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Algorithms for verifying deep neural networks
C. Liu, T. Arnon, C. Lazarus, C. Barrett, and M. J. Kochenderfer · 2019
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Verification of non-linear specifications for neural networks
C. Qin, B. O’Donoghue, R. Bunel, R. Stanforth, S. Gowal, J. Uesato, G. Swirszcz, P. Kohli, et al · 2019
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Accelerated first-order methods for hyperbolic programming
J. Renegar · 2019
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SE-Sync: a certifiably correct algorithm for synchronization over the special Euclidean group
D. M. Rosen, L. Carlone, A. S. Bandeira, and J. J. Leonard · 2019
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Provable nonconvex methods and algorithms (collection of papers)
J. Sun · 2019
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A conditional gradient-based augmented Lagrangian framework
A. Yurtsever, O. Fercoq, and V. Cevher · 2019
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Chordal decomposition in operator-splitting methods for sparse semidefinite programs
Y. Zheng, G. Fantuzzi, A. Papachristodoulou, P. Goulart, and A. Wynn · 2019
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