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Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians.
A. Y. Levin, “An algorithm for minimizing convex functions,” in Doklady Akademii Nauk , vol. 160, no. 6. Russian Academy of Sciences, 1965, pp. 1244–1247
1965
Earlier work this paper cites.
D. B. Yudin and A. S. Nemirovski, “Evaluation of the information complexity of mathematical programming problems,” Ekonomika i Matematicheskie Metody , vol. 12, pp. 128–142, 1976
1976
Earlier work this paper cites.
N. Z. Shor, “Cut-off method with space extension in convex programming problems,” Cybernetics , vol. 13, no. 1, pp. 94–96, 1977
1977
Earlier work this paper cites.
L. G. Khachiyan, “Polynomial algorithms in linear programming,” USSR Computational Mathematics and Mathematical Physics , vol. 20, no. 1, pp. 53–72, 1980
1980
Earlier work this paper cites.
K. G. Murty and S. N. Kabadi, “Some NP-complete problems in quadratic and nonlinear programming,” Mathematical Programming , vol. 39, no. 2, pp. 117–129, 1987
1987
Earlier work this paper cites.
L. G. Khachiyan, S. P. Tarasov, and I. Erlikh, “The method of inscribed ellipsoids,” in Soviet Math. Dokl , vol. 37, no. 1, 1988, pp. 226–230
1988
Earlier work this paper cites.
Y. Nesterov and A. Nemirovski, “Self-concordant functions and polynomial time methods in convex programming,” USSR Academy of Sciences, Central Economic&Mathematical Institute, Moscow , 1989
1989
Earlier work this paper cites.
P. M. Vaidya, “A new algorithm for minimizing convex functions over convex sets,” in 30th Annual Symposium on Foundations of Computer Science . IEEE Computer Society, 1989, pp. 338–343
1989
Earlier work this paper cites.
D. S. Atkinson and P. M. Vaidya, “A cutting plane algorithm for convex programming that uses analytic centers,” Mathematical Programming , vol. 69, no. 1, pp. 1–43, 1995
1995
Earlier work this paper cites.
P. A. Parrilo, “Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization,” Ph.D. dissertation, 2000
2000
Earlier work this paper cites.
J. B. Lasserre, “Global optimization with polynomials and the problem of moments,” SIAM Journal on optimization , vol. 11, no. 3, pp. 796–817, 2001
2001
Earlier work this paper cites.
F. Glover and S. Hanafi, “Tabu search and finite convergence,” Discrete Applied Mathematics , vol. 119, no. 1-2, pp. 3–36, 2002
2002
Earlier work this paper cites.
E. De Klerk and D. V. Pasechnik, “Approximation of the stability number of a graph via copositive programming,” SIAM Journal on Optimization , vol. 12, no. 4, pp. 875–892, 2002
2002
Earlier work this paper cites.
S. Boyd and L. Vandenberghe, “Convex Optimization,” 2004
2004
Earlier work this paper cites.
D. Bertsimas and S. Vempala, “Solving convex programs by random walks,” Journal of the ACM (JACM) , vol. 51, no. 4, pp. 540–556, 2004
2004
Earlier work this paper cites.
S. Boyd and L. Vandenberghe, “Localization and cutting-plane methods,” From Stanford EE 364b lecture notes , 2007
2007
Earlier work this paper cites.
K. K. Sivaramakrishnan and J. E. Mitchell, “Properties of a cutting plane method for semidefinite programming,” Pacific Journal of Optimization , vol. 8, pp. 779–802, 2007
2007
Earlier work this paper cites.
L. A. Rademacher, “Approximating the centroid is hard,” in Proceedings of the twenty-third annual symposium on Computational geometry , 2007, pp. 302–305
2007
Earlier work this paper cites.
S. Burer, “On the copositive representation of binary and continuous nonconvex quadratic programs,” Mathematical Programming , vol. 120, no. 2, p. 479–495, 2009
2009
Earlier work this paper cites.
D. Bertsekas, Convex optimization theory . Athena Scientific, 2009, vol. 1
2009
Earlier work this paper cites.
M. Dür, “Copositive programming–a survey,” in Recent advances in optimization and its applications in engineering . Springer, 2010, pp. 3–20
2010
Earlier work this paper cites.
J.-B. Hiriart-Urruty and A. Seeger, “A variational approach to copositive matrices,” SIAM review , vol. 52, no. 4, pp. 593–629, 2010
2010
Earlier work this paper cites.
M. W. Johnson, M. H. Amin, S. Gildert, T. Lanting, F. Hamze, N. Dickson, R. Harris, A. J. Berkley, J. Johansson, P. Bunyk et al. , “Quantum annealing with manufactured spins,” Nature , vol. 473, no. 7346, pp. 194–198, 2011
2011
Earlier work this paper cites.
S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein et al. , “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Foundations and Trends®in Machine learning , vol. 3, no. 1, pp. 1–122, 2011
2011
Earlier work this paper cites.
S. Burer, “Copositive programming,” in Handbook on semidefinite, conic and polynomial optimization . Springer, 2012, pp. 201–218
2012
Earlier work this paper cites.
H. Attouch, J. Bolte, and B. F. Svaiter, “Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods,” Mathematical Programming , vol. 137, no. 1, pp. 91–129, 2013
2013
Earlier work this paper cites.
M. Dür and J.-B. Hiriart-Urruty, “Testing copositivity with the help of difference-of-convex optimization,” Mathematical Programming , vol. 140, no. 1, pp. 31–43, 2013
2013
Earlier work this paper cites.
J. Bergstra, D. Yamins, and D. Cox, “Making a science of model search: Hyperparameter optimization in hundreds of dimensions for vision architectures,” in International conference on machine learning . Pmlr, 2013, pp. 115–123
2013
Cited alongside, same era.
2014
Cited alongside, same era.
A. Lucas, “Ising formulations of many NP problems,” Frontiers in physics , p. 5, 2014
2014
Cited alongside, same era.
T. F. Rønnow, Z. Wang, J. Job, S. Boixo, S. V. Isakov, D. Wecker, J. M. Martinis, D. A. Lidar, and M. Troyer, “Defining and detecting quantum speedup,” science , vol. 345, no. 6195, pp. 420–424, 2014
2014
Cited alongside, same era.
P. Hauke, H. G. Katzgraber, W. Lechner, H. Nishimori, and W. D. Oliver, “Perspectives of quantum annealing: Methods and implementations,” Reports on Progress in Physics , vol. 83, no. 5, p. 054401, 2020
2020
Later among the works it cites.
M. Willsch, D. Willsch, F. Jin, H. De Raedt, and K. Michielsen, “Benchmarking the quantum approximate optimization algorithm,” Quantum Information Processing , vol. 19, no. 7, pp. 1–24, 2020
2020
Later among the works it cites.
Y. R. Sanders, D. W. Berry, P. C. Costa, L. W. Tessler, N. Wiebe, C. Gidney, H. Neven, and R. Babbush, “Compilation of fault-tolerant quantum heuristics for combinatorial optimization,” PRX Quantum , vol. 1, no. 2, p. 020312, 2020
2020
Later among the works it cites.
S. Matsubara, M. Takatsu, T. Miyazawa, T. Shibasaki, Y. Watanabe, K. Takemoto, and H. Tamura, “Digital annealer for high-speed solving of combinatorial optimization problems and its applications,” in 2020 25th Asia and South Pacific Design Automation Conference (ASP-DAC) . IEEE, 2020, pp. 667–672
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Y. T. Lee, A. Sidford, and S. C.-w. Wong, “A faster cutting plane method and its implications for combinatorial and convex optimization,” in 2015 IEEE 56th Annual Symposium on Foundations of Computer Science . Ieee, 2015, pp. 1049–1065
2015
Cited alongside, same era.
2015
Cited alongside, same era.
D. Venturelli, D. Marchand, and G. Rojo, “Job shop scheduling solver based on quantum annealing,” in Proc. of ICAPS-16 Workshop on Constraint Satisfaction Techniques for Planning and Scheduling (COPLAS) , 2016, pp. 25–34
2016
Cited alongside, same era.
J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, “The theory of variational hybrid quantum-classical algorithms,” New Journal of Physics , vol. 18, no. 2, p. 023023, 2016
2016
Cited alongside, same era.
2016
Cited alongside, same era.
M. N. Bojnordi and E. Ipek, “Memristive boltzmann machine: A hardware accelerator for combinatorial optimization and deep learning,” in 2016 IEEE International Symposium on High Performance Computer Architecture (HPCA) . IEEE, 2016, pp. 1–13
2016
Cited alongside, same era.
P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara et al. , “A fully programmable 100-spin coherent ising machine with all-to-all connections,” Science , vol. 354, no. 6312, pp. 614–617, 2016
2016
Cited alongside, same era.
C. Brás, G. Eichfelder, and J. Júdice, “Copositivity tests based on the linear complementarity problem,” Computational Optimization and Applications , vol. 63, no. 2, pp. 461–493, 2016
2016
Cited alongside, same era.
2020
Later among the works it cites.
L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browaeys, G.-O. Reymond, and C. Jurczak, “Quantum computing with neutral atoms,” Quantum , vol. 4, p. 327, 2020
2020
Later among the works it cites.
W. Xia, J. C. Vera, and L. F. Zuluaga, “Globally solving nonconvex quadratic programs via linear integer programming techniques,” INFORMS Journal on Computing , vol. 32, no. 1, pp. 40–56, 2020
2020
Later among the works it cites.
T. Honjo, T. Sonobe, K. Inaba, T. Inagaki, T. Ikuta, Y. Yamada, T. Kazama, K. Enbutsu, T. Umeki, R. Kasahara et al. , “100,000-spin coherent Ising machine,” Science advances , vol. 7, no. 40, p. eabh0952, 2021
2021
Later among the works it cites.
2021
Later among the works it cites.
2021
Later among the works it cites.
S. Harwood, C. Gambella, D. Trenev, A. Simonetto, D. Bernal, and D. Greenberg, “Formulating and solving routing problems on quantum computers,” IEEE Transactions on Quantum Engineering , vol. 2, pp. 1–17, 2021
2021
Later among the works it cites.
M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio et al. , “Variational quantum algorithms,” Nature Reviews Physics , vol. 3, no. 9, pp. 625–644, 2021
2021
Later among the works it cites.
L. Bittel and M. Kliesch, “Training variational quantum algorithms is np-hard,” Physical review letters , vol. 127, no. 12, p. 120502, 2021
2021
Later among the works it cites.
A. Uvarov and J. D. Biamonte, “On barren plateaus and cost function locality in variational quantum algorithms,” Journal of Physics A: Mathematical and Theoretical , vol. 54, no. 24, p. 245301, 2021
2021
Later among the works it cites.
M. P. Harrigan, K. J. Sung, M. Neeley, K. J. Satzinger, F. Arute, K. Arya, J. Atalaya, J. C. Bardin, R. Barends, S. Boixo et al. , “Quantum approximate optimization of non-planar graph problems on a planar superconducting processor,” Nature Physics , vol. 17, no. 3, pp. 332–336, 2021
2021
Later among the works it cites.
M. Dür and F. Rendl, “Conic optimization: a survey with special focus on copositive optimization and binary quadratic problems,” EURO Journal on Computational Optimization , vol. 9, p. 100021, 2021
2021
Later among the works it cites.
2021
Later among the works it cites.
K. M. Anstreicher, “Testing copositivity via mixed–integer linear programming,” Linear Algebra and its Applications , vol. 609, pp. 218–230, 2021
2021
Later among the works it cites.
dwave-neal Documentation , D-Wave Systems Inc, 2021, available at https://docs.ocean.dwavesys.com/_/downloads/neal/en/latest/pdf/
2021
Later among the works it cites.
2021
Later among the works it cites.
2022
Closest in time.
A. Callison and N. Chancellor, “Hybrid quantum-classical algorithms in the noisy intermediate-scale quantum era and beyond,” Physical Review A , vol. 106, no. 1, p. 010101, 2022
2022
Closest in time.
N. Mohseni, P. L. McMahon, and T. Byrnes, “Ising machines as hardware solvers of combinatorial optimization problems,” Nature Reviews Physics , pp. 1–17, 2022
2022
Closest in time.
R. Badenbroek and E. de Klerk, “An analytic center cutting plane method to determine complete positivity of a matrix,” INFORMS Journal on Computing , vol. 34, no. 2, pp. 1115–1125, 2022
2022
Closest in time.
2022
Closest in time.
Gurobi Optimizer Reference Manual , 2022, available at http://www.gurobi.com
2022
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R. Quintero, D. Bernal, T. Terlaky, and L. F. Zuluaga, “Characterization of QUBO reformulations for the maximum k-colorable subgraph problem,” Quantum Information Processing , vol. 21, no. 3, pp. 1–36, 2022
2022
Closest in time.