Approximating Higher-Order Derivative Tensors Using Secant Updates

DOI10.1137/23m1549687arXiv2301.11678MaRDI QIDQ6195316

Unnamed Author, Raphael Hauser

Publication date: 13 March 2024

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.11678

zbMATH Keywords

quasi-Newton methodstensorssecant equationapproximate derivativessecant updateshigher-order optimization

Mathematics Subject Classification ID

Methods of quasi-Newton type (90C53) Numerical differentiation (65D25)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tensor Decompositions and Applications
• Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
• Convergence of quasi-Newton matrices generated by the symmetric rank one update
• Introductory lectures on convex optimization. A basic course.
• On the use of third-order models with fourth-order regularization for unconstrained optimization
• Cubic regularization of Newton method and its global performance
• Tensor Spaces and Numerical Tensor Calculus
• The convergence of variable metric matrices in unconstrained optimization
• On the Global Convergence of Broyden's Method
• Convergence Properties of a Class of Rank-two Updates
• Trust Region Methods
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• Accuracy and Stability of Numerical Algorithms
• Sharp Worst-Case Evaluation Complexity Bounds for Arbitrary-Order Nonconvex Optimization with Inexpensive Constraints
• A Class of Methods for Solving Nonlinear Simultaneous Equations
• A Rapidly Convergent Descent Method for Minimization
• Most Tensor Problems Are NP-Hard
• A Family of Variable-Metric Methods Derived by Variational Means
• A new approach to variable metric algorithms
• The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations
• Conditioning of Quasi-Newton Methods for Function Minimization
• A New Algorithm for Unconstrained Optimization

This page was built for publication: Approximating Higher-Order Derivative Tensors Using Secant Updates