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Sums of squares, moment matrices and optimization over polynomials

Citations

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Cited by:

  1. Cordian Riener & Thorsten Theobald & Lina Jansson Andrén & Jean B. Lasserre, 2013. "Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 122-141, February.
  2. Shenglong Hu & Guoyin Li & Liqun Qi, 2016. "A Tensor Analogy of Yuan’s Theorem of the Alternative and Polynomial Optimization with Sign structure," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 446-474, February.
  3. Jinyan Fan & Anwa Zhou, 2017. "A semidefinite algorithm for completely positive tensor decomposition," Computational Optimization and Applications, Springer, vol. 66(2), pages 267-283, March.
  4. Igor Klep & Markus Schweighofer, 2013. "An Exact Duality Theory for Semidefinite Programming Based on Sums of Squares," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 569-590, August.
  5. Gorissen, B.L. & den Hertog, D., 2012. "Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization," Other publications TiSEM 666c5307-4a4e-4be4-a0d0-b, Tilburg University, School of Economics and Management.
  6. P. M. Kleniati & P. Parpas & B. Rustem, 2010. "Decomposition-based Method for Sparse Semidefinite Relaxations of Polynomial Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 289-310, May.
  7. V. Jeyakumar & J. Vicente-Pérez, 2014. "Dual Semidefinite Programs Without Duality Gaps for a Class of Convex Minimax Programs," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 735-753, September.
  8. Adam Kurpisz & Samuli Leppänen & Monaldo Mastrolilli, 2017. "On the Hardest Problem Formulations for the 0/1 Lasserre Hierarchy," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 135-143, January.
  9. Peter Dickinson & Janez Povh, 2015. "On an extension of Pólya’s Positivstellensatz," Journal of Global Optimization, Springer, vol. 61(4), pages 615-625, April.
  10. Meng-Meng Zheng & Zheng-Hai Huang & Sheng-Long Hu, 2022. "Unconstrained minimization of block-circulant polynomials via semidefinite program in third-order tensor space," Journal of Global Optimization, Springer, vol. 84(2), pages 415-440, October.
  11. de Klerk, Etienne & Laurent, Monique, 2018. "Comparison of Lasserre's measure-based bounds for polynomial optimization to bounds obtained by simulated annealing," Other publications TiSEM 78f8f496-dc89-413e-864d-f, Tilburg University, School of Economics and Management.
  12. Xiao Wang & Xinzhen Zhang & Guangming Zhou, 2020. "SDP relaxation algorithms for $$\mathbf {P}(\mathbf {P}_0)$$P(P0)-tensor detection," Computational Optimization and Applications, Springer, vol. 75(3), pages 739-752, April.
  13. Philipp Renner & Karl Schmedders, 2017. "Dynamic Principal–Agent Models," Working Papers 203620456, Lancaster University Management School, Economics Department.
  14. Lulu Cheng & Xinzhen Zhang & Guyan Ni, 2021. "A semidefinite relaxation method for second-order cone tensor eigenvalue complementarity problems," Journal of Global Optimization, Springer, vol. 79(3), pages 715-732, March.
  15. de Klerk, Etienne & Laurent, Monique, 2019. "A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis," Other publications TiSEM d956492f-3e25-4dda-a5e2-e, Tilburg University, School of Economics and Management.
  16. Hyungjin Choi & Umesh Vaidya & Yongxin Chen, 2021. "A Convex Data-Driven Approach for Nonlinear Control Synthesis," Mathematics, MDPI, vol. 9(19), pages 1-12, October.
  17. Anwa Zhou & Xin Zhao & Jinyan Fan & Yanqin Bai, 2018. "Tensor maximal correlation problems," Journal of Global Optimization, Springer, vol. 70(4), pages 843-858, April.
  18. Jiawang Nie & Suhan Zhong, 2023. "Loss functions for finite sets," Computational Optimization and Applications, Springer, vol. 84(2), pages 421-447, March.
  19. Laurent, Monique & Vargas, Luis Felipe, 2022. "Finite convergence of sum-of-squares hierarchies for the stability number of a graph," Other publications TiSEM 3998b864-7504-4cf4-bc1d-f, Tilburg University, School of Economics and Management.
  20. Polyxeni-Margarita Kleniati & Panos Parpas & Berç Rustem, 2010. "Partitioning procedure for polynomial optimization," Journal of Global Optimization, Springer, vol. 48(4), pages 549-567, December.
  21. Etienne de Klerk & Monique Laurent, 2018. "Comparison of Lasserre’s Measure-Based Bounds for Polynomial Optimization to Bounds Obtained by Simulated Annealing," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1317-1325, November.
  22. Laurent, M. & Rostalski, P., 2012. "The approach of moments for polynomial equations," Other publications TiSEM f08f3cd2-b83e-4bf1-9322-a, Tilburg University, School of Economics and Management.
  23. Amir Ali Ahmadi & Georgina Hall, 2019. "On the Construction of Converging Hierarchies for Polynomial Optimization Based on Certificates of Global Positivity," Management Science, INFORMS, vol. 44(4), pages 1192-1207, November.
  24. V. Jeyakumar & G. Li & S. Srisatkunarajah, 2014. "Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations," Journal of Global Optimization, Springer, vol. 58(1), pages 31-50, January.
  25. Monique Laurent & Zhao Sun, 2014. "Handelman’s hierarchy for the maximum stable set problem," Journal of Global Optimization, Springer, vol. 60(3), pages 393-423, November.
  26. Jie Wang & Victor Magron, 2021. "Exploiting term sparsity in noncommutative polynomial optimization," Computational Optimization and Applications, Springer, vol. 80(2), pages 483-521, November.
  27. Tomohiko Mizutani & Makoto Yamashita, 2013. "Correlative sparsity structures and semidefinite relaxations for concave cost transportation problems with change of variables," Journal of Global Optimization, Springer, vol. 56(3), pages 1073-1100, July.
  28. Peter J. C. Dickinson & Janez Povh, 2019. "A new approximation hierarchy for polynomial conic optimization," Computational Optimization and Applications, Springer, vol. 73(1), pages 37-67, May.
  29. Varvitsiotis, A., 2013. "Combinatorial conditions for low rank solutions in semidefinite programming," Other publications TiSEM d0fcc572-daaf-4bd9-95db-1, Tilburg University, School of Economics and Management.
  30. O. Ferreira & A. Iusem & S. Németh, 2014. "Concepts and techniques of optimization on the sphere," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1148-1170, October.
  31. Feng Guo & Li Wang & Guangming Zhou, 2014. "Minimizing rational functions by exact Jacobian SDP relaxation applicable to finite singularities," Journal of Global Optimization, Springer, vol. 58(2), pages 261-284, February.
  32. T. D. Chuong & V. Jeyakumar & G. Li, 2019. "A new bounded degree hierarchy with SOCP relaxations for global polynomial optimization and conic convex semi-algebraic programs," Journal of Global Optimization, Springer, vol. 75(4), pages 885-919, December.
  33. Feng Guo & Liguo Jiao, 2021. "On solving a class of fractional semi-infinite polynomial programming problems," Computational Optimization and Applications, Springer, vol. 80(2), pages 439-481, November.
  34. de Klerk, Etienne & Laurent, Monique, 2017. "Comparison of Lasserre's Measure-based Bounds for Polynomial Optimization to Bounds Obtained by Simulated Annealing," Other publications TiSEM 7a865ba0-bffb-43fb-a376-7, Tilburg University, School of Economics and Management.
  35. Ruixue Zhao & Jinyan Fan, 2020. "Higher-degree tensor eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 799-816, April.
  36. Meilan Zeng, 2021. "Tensor Z-eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 78(2), pages 559-573, March.
  37. Jae Hyoung Lee & Liguo Jiao, 2018. "Solving Fractional Multicriteria Optimization Problems with Sum of Squares Convex Polynomial Data," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 428-455, February.
  38. O. P. Ferreira & S. Z. Németh, 2019. "On the spherical convexity of quadratic functions," Journal of Global Optimization, Springer, vol. 73(3), pages 537-545, March.
  39. Fook Wai Kong & Polyxeni-Margarita Kleniati & Berç Rustem, 2012. "Computation of Correlated Equilibrium with Global-Optimal Expected Social Welfare," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 237-261, April.
  40. de Klerk, E. & Laurent, M., 2010. "Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube," Other publications TiSEM 619d9658-77df-4b5e-9868-0, Tilburg University, School of Economics and Management.
  41. Sandra S. Y. Tan & Antonios Varvitsiotis & Vincent Y. F. Tan, 2021. "Analysis of Optimization Algorithms via Sum-of-Squares," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 56-81, July.
  42. Peter J. C. Dickinson & Janez Povh, 2013. "Moment Approximations for Set-Semidefinite Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 57-68, October.
  43. Kristijan Cafuta, 2019. "Sums of Hermitian squares decomposition of non-commutative polynomials in non-symmetric variables using NCSOStools," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 397-413, June.
  44. Anwa Zhou & Jinyan Fan, 2019. "A hierarchy of semidefinite relaxations for completely positive tensor optimization problems," Journal of Global Optimization, Springer, vol. 75(2), pages 417-437, October.
  45. Guanglei Wang & Hassan Hijazi, 2018. "Mathematical programming methods for microgrid design and operations: a survey on deterministic and stochastic approaches," Computational Optimization and Applications, Springer, vol. 71(2), pages 553-608, November.
  46. Sönke Behrends & Anita Schöbel, 2020. "Generating Valid Linear Inequalities for Nonlinear Programs via Sums of Squares," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 911-935, September.
  47. Jiawang Nie & Xinzhen Zhang, 2018. "Real eigenvalues of nonsymmetric tensors," Computational Optimization and Applications, Springer, vol. 70(1), pages 1-32, May.
  48. Marandi, Ahmadreza & Dahl, Joachim & de Klerk, Etienne, 2018. "A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem," Other publications TiSEM 981f1428-4d42-4d3f-9a7a-7, Tilburg University, School of Economics and Management.
  49. Sönke Behrends & Ruth Hübner & Anita Schöbel, 2018. "Norm bounds and underestimators for unconstrained polynomial integer minimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 73-107, February.
  50. Feng Guo & Xiaoxia Sun, 2020. "On semi-infinite systems of convex polynomial inequalities and polynomial optimization problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 669-699, April.
  51. Laurent, M. & Mourrain, B., 2009. "A generalized flat extension theorem for moment matrices," Other publications TiSEM de50ba38-97a8-419a-b1b1-3, Tilburg University, School of Economics and Management.
  52. Chen, Haibin & Li, Guoyin & Qi, Liqun, 2016. "Further results on Cauchy tensors and Hankel tensors," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 50-62.
  53. Papp, Dávid & Regős, Krisztina & Domokos, Gábor & Bozóki, Sándor, 2023. "The smallest mono-unstable convex polyhedron with point masses has 8 faces and 11 vertices," European Journal of Operational Research, Elsevier, vol. 310(2), pages 511-517.
  54. Gue Myung Lee & Tiến-Sơn Phạm, 2016. "Stability and Genericity for Semi-algebraic Compact Programs," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 473-495, May.
  55. Jinghao Zhu & Shangrui Zhao & Guohua Liu, 2014. "Solution to Global Minimization of Polynomials by Backward Differential Flow," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 828-836, June.
  56. Hayato Waki & Maho Nakata & Masakazu Muramatsu, 2012. "Strange behaviors of interior-point methods for solving semidefinite programming problems in polynomial optimization," Computational Optimization and Applications, Springer, vol. 53(3), pages 823-844, December.
  57. Ahmadreza Marandi & Joachim Dahl & Etienne Klerk, 2018. "A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem," Annals of Operations Research, Springer, vol. 265(1), pages 67-92, June.
  58. Anwa Zhou & Jinyan Fan, 2018. "Completely positive tensor recovery with minimal nuclear value," Computational Optimization and Applications, Springer, vol. 70(2), pages 419-441, June.
  59. V. Jeyakumar & J. B. Lasserre & G. Li, 2014. "On Polynomial Optimization Over Non-compact Semi-algebraic Sets," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 707-718, December.
  60. Bo Rao & Liu Yang & Jingmin Cai, 2025. "Optimal transport-based distributionally robust optimization with polynomial uncertainty," Journal of Global Optimization, Springer, vol. 93(1), pages 215-240, September.
  61. Eleftherios Couzoudis & Philipp Renner, 2013. "Computing generalized Nash equilibria by polynomial programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 459-472, June.
  62. Jinyan Fan & Anwa Zhou, 2016. "Computing the distance between the linear matrix pencil and the completely positive cone," Computational Optimization and Applications, Springer, vol. 64(3), pages 647-670, July.
  63. Laurent, Monique & Vargas, Luis, 2022. "On the exactness of sum-of-squares approximations for the cone of 5x5 copositive matrices," Other publications TiSEM 39e7a789-52b4-4910-a78c-d, Tilburg University, School of Economics and Management.
  64. Gorissen, B.L. & den Hertog, D., 2012. "Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization," Discussion Paper 2012-031, Tilburg University, Center for Economic Research.
  65. Hao Hu & Renata Sotirov, 2021. "The linearization problem of a binary quadratic problem and its applications," Annals of Operations Research, Springer, vol. 307(1), pages 229-249, December.
  66. Fook Kong & Berç Rustem, 2013. "Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity," Journal of Global Optimization, Springer, vol. 57(1), pages 251-277, September.
  67. Gribling, Sander & Laat, David de & Laurent, Monique, 2017. "Lower Bounds on Matrix Factorization Ranks via Noncommutative Polynomial Optimization," Other publications TiSEM 2dddf156-3d4b-4936-bf02-a, Tilburg University, School of Economics and Management.
  68. Shenglong Hu & Guoyin Li, 2021. "$${\text {B}}$$ B -subdifferentials of the projection onto the matrix simplex," Computational Optimization and Applications, Springer, vol. 80(3), pages 915-941, December.
  69. Anwa Zhou & Jinyan Fan, 2015. "Interiors of completely positive cones," Journal of Global Optimization, Springer, vol. 63(4), pages 653-675, December.
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