Analysis of the Barzilai-Borwein Step-Sizes for Problems in Hilbert Spaces

Behzad Azmi () and Karl Kunisch ()
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Behzad Azmi: Austrian Academy of Science
Karl Kunisch: Austrian Academy of Science

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 3, No 8, 819-844

Abstract: Abstract The Barzilai and Borwein gradient method has received a significant amount of attention in different fields of optimization. This is due to its simplicity, computational cheapness, and efficiency in practice. In this research, based on spectral analysis techniques, root-linear global convergence for the Barzilai and Borwein method is proven for strictly convex quadratic problems posed in infinite-dimensional Hilbert spaces. The applicability of these results is demonstrated for two optimization problems governed by partial differential equations.

Keywords: Barzilai–Borwein method; Hilbert spaces; R-Linear rate of convergence; PDE-constrained optimization; 65K05; 49J20; 49K20; 93C20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01677-y

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