On the steplength selection in gradient methods for unconstrained optimization

Daniela di Serafino, Valeria Ruggiero, Gerardo Toraldo and Luca Zanni

Applied Mathematics and Computation, 2018, vol. 318, issue C, 176-195

Abstract: The seminal paper by Barzilai and Borwein (1988) has given rise to an extensive investigation, leading to the development of effective gradient methods. Several steplength rules have been first designed for unconstrained quadratic problems and then extended to general nonlinear optimization problems. These rules share the common idea of attempting to capture, in an inexpensive way, some second-order information. However, the convergence theory of the gradient methods using the previous rules does not explain their effectiveness, and a full understanding of their practical behaviour is still missing. In this work we investigate the relationships between the steplengths of a variety of gradient methods and the spectrum of the Hessian of the objective function, providing insight into the computational effectiveness of the methods, for both quadratic and general unconstrained optimization problems. Our study also identifies basic principles for designing effective gradient methods.

Keywords: Gradient methods; Steplength selection; Hessian spectral properties (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:318:y:2018:i:c:p:176-195

DOI: 10.1016/j.amc.2017.07.037

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