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Cubic regularization of Newton method and its global performance

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  1. 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.
  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. 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.
  5. 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.
  6. 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.
  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. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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).
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  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. 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.
  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. 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.
  34. 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.
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