Abstract
The aim of this paper is the study of different approaches to combine and scale, in an efficient manner, descent information for the solution of unconstrained optimization problems. We consider the situation in which different directions are available in a given iteration, and we wish to analyze how to combine these directions in order to provide a method more efficient and robust than the standard Newton approach. In particular, we will focus on the scaling process that should be carried out before combining the directions. We derive some theoretical results regarding the conditions necessary to ensure the convergence of combination procedures following schemes similar to our proposals. Finally, we conduct some computational experiments to compare these proposals with a modified Newton’s method and other procedures in the literature for the combination of information.
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Catarina P. Avelino was partially supported by Portuguese FCT postdoctoral grant SFRH/BPD/20453/2004 and by the Research Unit CM-UTAD of University of Trás-os-Montes e Alto Douro. Javier M. Moguerza and Alberto Olivares were partially supported by Spanish grant MEC MTM2006-14961-C05-05.
Francisco J. Prieto was partially supported by grant MTM2007-63140 of the Spanish Ministry of Education.
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Avelino, C.P., Moguerza, J.M., Olivares, A. et al. Combining and scaling descent and negative curvature directions. Math. Program. 128, 285–319 (2011). https://doi.org/10.1007/s10107-009-0305-6
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DOI: https://doi.org/10.1007/s10107-009-0305-6