Journal Article10.1007/S10107-006-0706-8
Cubic regularization of Newton method and its global performance
Yurii Nesterov,Boris T. Polyak +1 more
1.2K
TL;DR: This paper provides theoretical analysis for a cubic regularization of Newton method as applied to unconstrained minimization problem and proves general local convergence results for this scheme.
read more
Abstract: In this paper, we provide theoretical analysis for a cubic regularization of Newton method as applied to unconstrained minimization problem. For this scheme, we prove general local convergence results. However, the main contribution of the paper is related to global worst-case complexity bounds for different problem classes including some nonconvex cases. It is shown that the search direction can be computed by standard linear algebra technique.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Journal Article
Towards Sharp Stochastic Zeroth Order Hessian Estimators over Riemannian Manifolds
TL;DR: These results provide the first bias bound for Hessian estimators that explicitly depends on the geometry of the underlying Riemannian manifold.
1
Global Convergence of Two-Timescale Actor-Critic for Solving Linear Quadratic Regulator
TL;DR: In this article , the authors investigate the single-sample two-timescale actor-critic (AC) for solving the canonical linear quadratic regulator (LQR) problem, where the actor and the critic update only once with a single sample in each iteration.
Accelerated Stochastic Optimization Methods under Quasar-convexity
Qiang Fu,Ashia Wilson +1 more
- 08 May 2023
TL;DR: In this paper , a stochastic algorithm for minimizing quasar-convex functions is proposed. But it is not a deterministic algorithm, and it has high complexity and slow convergence.
1
•Posted Content
Radial Duality Part II: Applications and Algorithms.
TL;DR: In this article, the radial subgradient, smoothing, and accelerated methods were proposed to solve a range of constrained convex and non-convex optimization problems and that can scale-up more efficiently than their classic counterparts.
1
Riemannian Stochastic Variance-Reduced Cubic Regularized Newton Method for Submanifold Optimization
TL;DR: In this article , a stochastic variance-reduced cubic regularized Newton algorithm is proposed to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space.
References
A method for the solution of certain non – linear problems in least squares
TL;DR: In this article, the problem of least square problems with non-linear normal equations is solved by an extension of the standard method which insures improvement of the initial solution, which can also be considered an extension to Newton's method.
•Book
Practical Methods of Optimization
Roger Fletcher
- 01 Jan 2009
TL;DR: The aim of this book is to provide a Discussion of Constrained Optimization and its Applications to Linear Programming and Other Optimization Problems.
9.3K
•Book
Numerical methods for unconstrained optimization and nonlinear equations
John E. Dennis,Robert B. Schnabel +1 more
- 01 Mar 1983
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
8.2K