Quasi Newton techniques generate identical points II: The proofs of four new theorems

DOI10.1007/BF01585007zbMath0252.90053MaRDI QIDQ5666403

L. C. W. Dixon

Publication date: 1972

Published in: Mathematical Programming (Search for Journal in Brave)

Mathematics Subject Classification ID

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

Related Items (9)

Rates of superlinear convergence for classical quasi-Newton methods ⋮ Nonsmooth optimization via quasi-Newton methods ⋮ Degenerate values for Broyden methods ⋮ Towards explicit superlinear convergence rate for SR1 ⋮ On the convergence, invariance, and related aspects of a modification of Huang's algorithm ⋮ Updating of conjugate direction matrices using members of Broyden's family ⋮ Unified approach to unconstrained minimization via basic matrix factorizations ⋮ New results on superlinear convergence of classical quasi-Newton methods ⋮ A family of variable metric updates

Cites Work

• Unified approach to quadratically convergent algorithms for function minimization
• Variable metric algorithms: Necessary and sufficient conditions for identical behaviour of nonquadratic functions
• A Rapidly Convergent Descent Method for Minimization
• A minimal point of a finite metric set
• Quasi-Newton Methods and their Application to Function Minimisation
• A Family of Variable-Metric Methods Derived by Variational Means
• Computational experience with quadratically convergent minimisation methods
• Variations on Variable-Metric Methods
• 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
• Conditioning of Quasi-Newton Methods for Function Minimization
• Optimal Conditioning of Quasi-Newton Methods
• Quasi-newton algorithms generate identical points

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