A modified BFGS method and its superlinear convergence in nonconvex minimization with general line search rule

DOI10.1007/s12190-008-0117-5zbMath1170.65048OpenAlexW2010088179MaRDI QIDQ949372

Qiang Guo, Dan-Hong Wang, Jian-guo Liu

Publication date: 21 October 2008

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-008-0117-5

zbMATH Keywords

unconstrained optimizationglobal convergenceline searchsuper-linear convergenceBroyden-Fletcher-Goldfarb-Shanno (BFGS) methodmodified BFGS

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26)

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Cites Work

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• Über die globale Konvergenz von Variable-Metrik-Verfahren mit nicht- exakter Schrittweitenbestimmung
• The BFGS method with exact line searches fails for non-convex objective functions
• An ABS algorithm for solving singular nonlinear systems with rank defects.
• Global convergence properties of the modified BFGS method associating with general line search model
• An effective algorithm for minimization
• Minimization of functions having Lipschitz continuous first partial derivatives
• Variable metric algorithms: Necessary and sufficient conditions for identical behaviour of nonquadratic functions
• Global Convergence of a Cass of Quasi-Newton Methods on Convex Problems
• A Tool for the Analysis of Quasi-Newton Methods with Application to Unconstrained Minimization
• Quasi-Newton Methods, Motivation and Theory
• Convergence Conditions for Ascent Methods
• Variable metric methods of minimisation
• On the Convergence of the Variable Metric Algorithm