Full Convergence of Regularized Methods for Unconstrained Optimization
Published Online:15 Oct 2026https://doi.org/10.1287/moor.2025.1082
References
- [1] (1998) On the projected subgradient method for nonsmooth convex optimization in a Hilbert space. Math. Programming 81:23–35.Crossref, Google Scholar
- [2] (1999) Nonlinear Programming (Athena Scientific, Belmont, MA).Google Scholar
- [3] (2015) Convex Optimization Algorithms (Athena Scientific, Belmont, MA).Google Scholar
- [4] (2017) Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. Math. Programming 163:359–368.Crossref, Google Scholar
- [5] (1995) Full convergence of the steepest descent method with inexact line searches. Optim. 32(2):137–146.Crossref, Google Scholar
- [6] (2011) Adaptive cubic regularisation methods for unconstrained optimization. Part I: Motivation, convergence and numerical results. Math. Programming 127(2):245–295.Crossref, Google Scholar
- [7] (2011) Adaptive cubic regularisation methods for unconstrained optimization. Part II: Worst-case function-and derivative-evaluation complexity. Math. Programming 130(2):295–319.Crossref, Google Scholar
- [8] (2012) Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization. Optim. Methods Software 27(2):197–219.Crossref, Google Scholar
- [9] (2017) Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients. Optim. Methods Software 32(6):1273–1298.Crossref, Google Scholar
- [10] (2019) Universal regularization methods: Varying the power, the smoothness and the accuracy. SIAM J. Optim. 29(1):595–615.Crossref, Google Scholar
- [11] (2001) Quasi-Fejérian analysis of some optimization algorithms. Butnariu D, Censor Y, Reich S, eds. Volume 8: Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, Studies in Computational Mathematics, vol. 8 (Elsevier, New York), 115–152.Google Scholar
- [12] (2013) Variable metric quasi-Fejér monotonicity. Nonlinear Anal. Theory Methods Appl. 78:17–31.Crossref, Google Scholar
- [13] (2005) A steepest descent method for vector optimization. J. Comput. Appl. Math. 175(2):395–414.Crossref, Google Scholar
- [14] (2022) A cubic regularization of Newton’s method with finite difference Hessian approximations. Numerical Algorithms 90(2):607–630.Crossref, Google Scholar
- [15] (2003) On the convergence properties of the projected gradient method for convex optimization. Comput. Appl. Math. 22(1):37–52.Crossref, Google Scholar
- [16] (1994) Entropy-like proximal methods in convex programming. Math. Oper. Res. 19(4):790–814.Link, Google Scholar
- [17] (2022) Diagonal BFGS updates and applications to the limited memory BFGS method. Comput. Optim. Appl. 81(3):829–856.Crossref, Google Scholar
- [18] (2013) Introductory Lectures on Convex Optimization: A Basic Course, vol. 87 (Springer Science & Business Media, New York).Google Scholar
- [19] (2006) Cubic regularization of Newton method and its global performance. Math. Programming 108(1):177–205.Crossref, Google Scholar
- [20] (2006) Numerical Optimization (Springer, New York).Crossref, Google Scholar
- [21] (1987) Introduction to Optimization (Optimization Software, New York).Google Scholar

