On the relation between quadratic termination and convergence properties of minimization algorithms. Part I. Theory

DOI10.1007/BF01389973zbMath0366.65027OpenAlexW93171880MaRDI QIDQ1241969

Josef Stoer

Publication date: 1977

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132492

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Nonlinear programming (90C30)

Related Items (10)

Nonlinear conjugate gradient methods for the optimal control of laser surface hardening ⋮ A generalized conjugate gradient algorithm for minimization ⋮ On the stable global convergence of particular quasi-newton-methods ⋮ Quasi-Newton-Verfahren vom Rang-Eins-Typ zur Lösung unrestringierter Minimierungsprobleme. I: Verfahren und grundlegende Eigenschaften ⋮ Quasi-Newton-Verfahren vom Rang-Eins-Typ zur Lösung unrestringierter Minimierungsprobleme. II: n-Schritt-quadratische Konvergenz für Restart-Varianten ⋮ Superlinear convergence of symmetric Huang's class of methods ⋮ Unnamed Item ⋮ Imperfect conjugate gradient algorithms for extended quadratic functions ⋮ On the relation between quadratic termination and convergence properties of minimization algorithms. Part II. Applications ⋮ A derivative-based bracketing scheme for univariate minimization and the conjugate gradient method

Cites Work

• Alternative proofs of the convergence properties of the conjugate- gradient method
• Die Konvergenzordnung des Fletcher-Powell-Algorithmus
• Variable Metric Method for Minimization
• Self-Scaling Variable Metric (SSVM) Algorithms
• Self-Scaling Variable Metric (SSVM) Algorithms
• Convergence conditions for restarted conjugate gradient methods with inaccurate line searches
• Practical convergence conditions for the Davidon-Fletcher-Powell method
• On the convergence rate of imperfect minimization algorithms in Broyden'sβ-class
• Quasi-Newton Methods, Motivation and Theory
• Rate of Convergence of Several Conjugate Gradient Algorithms
• On the Local and Superlinear Convergence of Quasi-Newton Methods
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• A Rapidly Convergent Descent Method for Minimization
• Function minimization by conjugate gradients
• The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
• Quasi-Newton Methods and their Application to Function Minimisation
• Variable metric methods of minimisation
• A new approach to variable metric algorithms
• On the Convergence of the Variable Metric Algorithm
• The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations
• Methods of conjugate directions versus quasi-Newton methods
• Practical convergence conditions for unconstrained optimization
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