Global and superlinear convergence of an algorithm for one-dimensional minimization of convex functions

DOI10.1007/BF01585109zbMath0505.90064MaRDI QIDQ4742570

Robert Mifflin, Claude Lemaréchal

Publication date: 1982

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

zbMATH Keywords

nonsmooth optimizationpolyhedral approximationsubgradientsuperlinear convergencequadratic approximationunconstrained minimization problempolyhedral methodunivariate optimizationlocal piece-wise linear approximation

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Rate of convergence, degree of approximation (41A25)

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Cites Work

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• Newton's method for convex programming and Tschebyscheff approximation
• Steplength algorithms for minimizing a class of nondifferentiable functions
• The Cutting-Plane Method for Solving Convex Programs
• A Superlinearly Convergent Algorithm for One-Dimensional Constrained Minimization Problems with Convex Functions
• A modification and an extension of Lemarechal’s algorithm for nonsmooth minimization
• Convex Analysis