Asymptotic behaviour of a family of gradient algorithms in \(\mathbb R^{ d }\) and Hilbert spaces

DOI10.1007/s10107-005-0602-7zbMath1111.90085arXiv0802.4382OpenAlexW2075556305WikidataQ61855870 ScholiaQ61855870MaRDI QIDQ2492701

Anatoly A. Zhigljavsky, Luc Pronzato, Henry P. Wynn

Publication date: 14 June 2006

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.4382

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Convex programming (90C25) Programming in abstract spaces (90C48)

Related Items (7)

An asymptotically optimal gradient algorithm for quadratic optimization with low computational cost ⋮ Estimation of spectral bounds in gradient algorithms ⋮ Delayed Gradient Methods for Symmetric and Positive Definite Linear Systems ⋮ Gradient algorithms for quadratic optimization with fast convergence rates ⋮ Fast gradient methods with alignment for symmetric linear systems without using Cauchy step ⋮ Optimal experimental design and some related control problems ⋮ On the asymptotic convergence and acceleration of gradient methods

Cites Work

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• On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method
• On the behavior of the gradient norm in the steepest descent method
• On the asymptotic directions of the s-dimensional optimum gradient method
• Kantorovich-type inequalities for operators via \(D\)-optimal design theory
• The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
• The Equivalence of Two Extremum Problems
• Two-Point Step Size Gradient Methods
• A spectral conjugate gradient method for unconstrained optimization
• Renormalised steepest descent in Hilbert space converges to a two-point attractor.
• Relaxed steepest descent and Cauchy-Barzilai-Borwein method

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