IDEAS home Printed from https://ideas.repec.org/r/cor/louvrp/1927.html

Cubic regularization of Newton method and its global performance

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as


Cited by:

  1. Danqing Zhou & Shiqian Ma & Junfeng Yang, 2026. "AdaBB: Adaptive Barzilai-Borwein Method for Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 51(1), pages 715-745, January.
  2. Nesterov, Yurii, 2022. "Quartic Regularity," LIDAM Discussion Papers CORE 2022001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Sergey Guminov & Alexander Gasnikov & Ilya Kuruzov, 2023. "Accelerated methods for weakly-quasi-convex optimization problems," Computational Management Science, Springer, vol. 20(1), pages 1-19, December.
  4. Qinsi Wang & Wei Hong Yang, 2024. "An adaptive regularized proximal Newton-type methods for composite optimization over the Stiefel manifold," Computational Optimization and Applications, Springer, vol. 89(2), pages 419-457, November.
  5. Yassine Nabou & Ion Necoara, 2024. "Efficiency of higher-order algorithms for minimizing composite functions," Computational Optimization and Applications, Springer, vol. 87(2), pages 441-473, March.
  6. Hande Benson & David Shanno, 2014. "Interior-point methods for nonconvex nonlinear programming: cubic regularization," Computational Optimization and Applications, Springer, vol. 58(2), pages 323-346, June.
  7. Liaoyuan Zeng & Ting Kei Pong, 2022. "$$\rho$$ ρ -regularization subproblems: strong duality and an eigensolver-based algorithm," Computational Optimization and Applications, Springer, vol. 81(2), pages 337-368, March.
  8. Ion Necoara & Flavia Chorobura, 2025. "Efficiency of Stochastic Coordinate Proximal Gradient Methods on Nonseparable Composite Optimization," Mathematics of Operations Research, INFORMS, vol. 50(2), pages 993-1018, May.
  9. Kenji Ueda & Nobuo Yamashita, 2010. "On a Global Complexity Bound of the Levenberg-Marquardt Method," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 443-453, December.
  10. Jaroslav Fowkes & Nicholas Gould & Chris Farmer, 2013. "A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions," Journal of Global Optimization, Springer, vol. 56(4), pages 1791-1815, August.
  11. Roberto Andreani & Gabriel Haeser & Renan William Prado & Maria L. Schuverdt & Leonardo D. Secchin, 2025. "Global Convergence of a Second-order Augmented Lagrangian Method Under an Error Bound Condition," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-30, August.
  12. Fedor Stonyakin & Ilya Kuruzov & Boris Polyak, 2023. "Stopping Rules for Gradient Methods for Non-convex Problems with Additive Noise in Gradient," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 531-551, August.
  13. Dewei Zhang & Sam Davanloo Tajbakhsh, 2023. "Riemannian Stochastic Variance-Reduced Cubic Regularized Newton Method for Submanifold Optimization," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 324-361, January.
  14. Dmitry Kamzolov & Klea Ziu & Artem Agafonov & Martin Takáč, 2026. "Accelerated Adaptive Cubic Regularized Quasi-Newton Methods," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-46, January.
  15. Boris Polyak & Andrey Tremba, 2020. "Sparse solutions of optimal control via Newton method for under-determined systems," Journal of Global Optimization, Springer, vol. 76(3), pages 613-623, March.
  16. S. Gratton & Ph. L. Toint, 2023. "OFFO minimization algorithms for second-order optimality and their complexity," Computational Optimization and Applications, Springer, vol. 84(2), pages 573-607, March.
  17. Tuyen Trung Truong & Tat Dat To & Hang-Tuan Nguyen & Thu Hang Nguyen & Hoang Phuong Nguyen & Maged Helmy, 2023. "A Fast and Simple Modification of Newton’s Method Avoiding Saddle Points," Journal of Optimization Theory and Applications, Springer, vol. 199(2), pages 805-830, November.
  18. Anton Rodomanov & Yurii Nesterov, 2020. "Smoothness Parameter of Power of Euclidean Norm," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 303-326, May.
  19. Yurii Nesterov, 2021. "Superfast Second-Order Methods for Unconstrained Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 1-30, October.
  20. Aimi, A. & Leoni, M.A. & Remogna, S., 2024. "Numerical solution of nonlinear Fredholm–Hammerstein integral equations with logarithmic kernel by spline quasi-interpolating projectors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 183-194.
  21. Silvia Berra & Alessandro Torraca & Federico Benvenuto & Sara Sommariva, 2024. "Combined Newton-Gradient Method for Constrained Root-Finding in Chemical Reaction Networks," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 404-427, January.
  22. Ariizumi, Shumpei & Yamakawa, Yuya & Yamashita, Nobuo, 2024. "Convergence properties of Levenberg–Marquardt methods with generalized regularization terms," Applied Mathematics and Computation, Elsevier, vol. 463(C).
  23. Jianyu Xiao & Haibin Zhang & Huan Gao, 2025. "A Chebyshev–Halley Method with Gradient Regularization and an Improved Convergence Rate," Mathematics, MDPI, vol. 13(8), pages 1-17, April.
  24. J. M. Martínez & L. T. Santos, 2022. "On large-scale unconstrained optimization and arbitrary regularization," Computational Optimization and Applications, Springer, vol. 81(1), pages 1-30, January.
  25. Francisco Facchinei & Vyacheslav Kungurtsev & Lorenzo Lampariello & Gesualdo Scutari, 2021. "Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 595-627, May.
  26. Seonho Park & Seung Hyun Jung & Panos M. Pardalos, 2020. "Combining Stochastic Adaptive Cubic Regularization with Negative Curvature for Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 953-971, March.
  27. Tianyu Wang & Yasong Feng, 2024. "Convergence Rates of Zeroth Order Gradient Descent for Łojasiewicz Functions," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1611-1633, December.
  28. Xihua Zhu & Jiangze Han & Bo Jiang, 2022. "An adaptive high order method for finding third-order critical points of nonconvex optimization," Journal of Global Optimization, Springer, vol. 84(2), pages 369-392, October.
  29. Nadav Hallak & Marc Teboulle, 2020. "Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 480-503, August.
  30. Kenji Ueda & Nobuo Yamashita, 2012. "Global Complexity Bound Analysis of the Levenberg–Marquardt Method for Nonsmooth Equations and Its Application to the Nonlinear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 450-467, February.
  31. Jian Chen & Wang Chen & Liping Tang & Xinmin Yang, 2026. "Preconditioned Barzilai-Borwein Methods for Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 208(1), pages 1-43, January.
  32. Yurii Nesterov, 2024. "Set-Limited Functions and Polynomial-Time Interior-Point Methods," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 11-26, July.
  33. Shun Arahata & Takayuki Okuno & Akiko Takeda, 2023. "Complexity analysis of interior-point methods for second-order stationary points of nonlinear semidefinite optimization problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 555-598, November.
  34. Mine Aylin Bayrak & Ali Demir & Ebru Ozbilge, 2022. "On Fractional Newton‐Type Method for Nonlinear Problems," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
  35. Ba Khiet Le & Minh N. Dao & Michel A. Théra, 2025. "Solving Non-Monotone Inclusions Using Monotonicity of Pairs of Operators," Journal of Optimization Theory and Applications, Springer, vol. 207(1), pages 1-19, October.
  36. Rujun Jiang & Man-Chung Yue & Zhishuo Zhou, 2021. "An accelerated first-order method with complexity analysis for solving cubic regularization subproblems," Computational Optimization and Applications, Springer, vol. 79(2), pages 471-506, June.
  37. Jiaxiang Li & Krishnakumar Balasubramanian & Shiqian Ma, 2023. "Stochastic Zeroth-Order Riemannian Derivative Estimation and Optimization," Mathematics of Operations Research, INFORMS, vol. 48(2), pages 1183-1211, May.
  38. Weiwei Kong & Jefferson G. Melo & Renato D. C. Monteiro, 2020. "An efficient adaptive accelerated inexact proximal point method for solving linearly constrained nonconvex composite problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 305-346, June.
  39. Giovanni Fasano & Raffaele Pesenti, 2017. "Conjugate Direction Methods and Polarity for Quadratic Hypersurfaces," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 764-794, December.
  40. Adeyemi D. Adeoye & Alberto Bemporad, 2023. "SCORE: approximating curvature information under self-concordant regularization," Computational Optimization and Applications, Springer, vol. 86(2), pages 599-626, November.
  41. Van-Bong Nguyen, 2025. "Solving a generalization of the p-regularized subproblems by matrix simultaneous diagonalization via congruence," Journal of Global Optimization, Springer, vol. 93(2), pages 523-534, October.
  42. Debdas Ghosh, 2025. "Cubic Regularization Technique of the Newton Method for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 207(2), pages 1-44, November.
  43. Jiulin Wang & Mengmeng Song & Yong Xia, 2022. "On Local Nonglobal Minimum of Trust-Region Subproblem and Extension," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 707-722, November.
  44. Nikita Doikov & Yurii Nesterov, 2021. "Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 317-339, April.
  45. A. L. Custódio & R. Garmanjani & M. Raydan, 2024. "Derivative-free separable quadratic modeling and cubic regularization for unconstrained optimization," 4OR, Springer, vol. 22(1), pages 121-144, March.
  46. Shuyao Li & Stephen J. Wright, 2025. "A Randomized Algorithm for Nonconvex Minimization With Inexact Evaluations and Complexity Guarantees," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-27, December.
  47. Ana Luísa Custódio & Youssef Diouane & Rohollah Garmanjani & Elisa Riccietti, 2021. "Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 73-93, January.
  48. Naoki Marumo & Takayuki Okuno & Akiko Takeda, 2023. "Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares," Computational Optimization and Applications, Springer, vol. 84(3), pages 833-874, April.
  49. Elizabeth Karas & Sandra Santos & Benar Svaiter, 2015. "Algebraic rules for quadratic regularization of Newton’s method," Computational Optimization and Applications, Springer, vol. 60(2), pages 343-376, March.
  50. Glaydston Bento & Boris Mordukhovich & Tiago Mota & Yurii Nesterov, 2025. "Convergence of Descent Optimization Algorithms under Polyak-Łojasiewicz-Kurdyka Conditions," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-29, December.
  51. S. Gratton & C.-K. Sim & Ph. L. Toint, 2025. "Refining asymptotic complexity bounds for nonconvex optimization methods, including why steepest descent is $$o(\epsilon ^{-2})$$ rather than $$\mathcal{O}(\epsilon ^{-2})$$," Computational Optimization and Applications, Springer, vol. 92(2), pages 515-527, November.
  52. Quoc Tran-Dinh & Ling Liang & Kim-Chuan Toh, 2022. "A New Homotopy Proximal Variable-Metric Framework for Composite Convex Minimization," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 508-539, February.
  53. Alkousa, Mohammad & Stonyakin, Fedor & Gasnikov, Alexander & Abdo, Asmaa & Alcheikh, Mohammad, 2024. "Higher degree inexact model for optimization problems," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
  54. Nicholas I. M. Gould & Tyrone Rees & Jennifer A. Scott, 2019. "Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems," Computational Optimization and Applications, Springer, vol. 73(1), pages 1-35, May.
  55. Geovani N. Grapiglia & Ekkehard W. Sachs, 2017. "On the worst-case evaluation complexity of non-monotone line search algorithms," Computational Optimization and Applications, Springer, vol. 68(3), pages 555-577, December.
  56. Robert Gower & Dirk A. Lorenz & Maximilian Winkler, 2024. "A Bregman–Kaczmarz method for nonlinear systems of equations," Computational Optimization and Applications, Springer, vol. 87(3), pages 1059-1098, April.
  57. Hongcheng Liu & Yinyu Ye & Hung Yi Lee, 2022. "High-Dimensional Learning Under Approximate Sparsity with Applications to Nonsmooth Estimation and Regularized Neural Networks," Operations Research, INFORMS, vol. 70(6), pages 3176-3197, November.
  58. Chuan He & Heng Huang & Zhaosong Lu, 2024. "A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization," Computational Optimization and Applications, Springer, vol. 89(3), pages 843-894, December.
  59. Yuquan Chen & Yunkang Sun & Bing Wang, 2023. "Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme," Mathematics, MDPI, vol. 11(22), pages 1-16, November.
  60. Geovani Nunes Grapiglia & Jinyun Yuan & Ya-xiang Yuan, 2016. "Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 980-997, December.
  61. Yamakawa, Yuya & Yamashita, Nobuo, 2025. "Convergence analysis of a regularized Newton method with generalized regularization terms for unconstrained convex optimization problems," Applied Mathematics and Computation, Elsevier, vol. 491(C).
  62. Nesterov, Yurii, 2024. "High-Order Reduced-Gradient Methods for Composite Variational Inequalities," LIDAM Discussion Papers CORE 2024025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  63. Chenyu Zhang & Rujun Jiang, 2025. "Riemannian Adaptive Regularized Newton Methods with Hölder Continuous Hessians," Computational Optimization and Applications, Springer, vol. 92(1), pages 29-79, September.
  64. Yuning Jiang & Dimitris Kouzoupis & Haoyu Yin & Moritz Diehl & Boris Houska, 2021. "Decentralized Optimization Over Tree Graphs," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 384-407, May.
  65. Yonggang Pei & Shaofang Song & Detong Zhu, 2023. "A sequential adaptive regularisation using cubics algorithm for solving nonlinear equality constrained optimization," Computational Optimization and Applications, Springer, vol. 84(3), pages 1005-1033, April.
  66. Jalaj Bhandari & Daniel Russo, 2024. "Global Optimality Guarantees for Policy Gradient Methods," Operations Research, INFORMS, vol. 72(5), pages 1906-1927, September.
  67. Oliver Hinder & Yinyu Ye, 2024. "Worst-Case Iteration Bounds for Log Barrier Methods on Problems with Nonconvex Constraints," Mathematics of Operations Research, INFORMS, vol. 49(4), pages 2402-2424, November.
  68. Nhung Hong Nguyen & Thanh Quoc Trinh & Phan Tu Vuong, 2026. "The Projected Heavy-ball Method for Quasar-monotone Variational Inequalities and Quasar-convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 208(2), pages 1-29, February.
  69. Meijia Yang & Shu Wang & Yong Xia, 2022. "Toward Nonquadratic S-Lemma: New Theory and Application in Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 353-363, July.
  70. Hong Zhu & Yunhai Xiao, 2024. "A hybrid inexact regularized Newton and negative curvature method," Computational Optimization and Applications, Springer, vol. 88(3), pages 849-870, July.
  71. Kenji Ueda & Nobuo Yamashita, 2014. "A regularized Newton method without line search for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 59(1), pages 321-351, October.
IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.