In recent years several proposals for the step-size selection have largely improved the gradient methods, in the case of both constrained and unconstrained nonlinear optimization. We introduce a new step-size rule with some crucial properties. We design step-size selection strategies where the new rule and a standard Barzilai-Borwein (BB) rule can be adaptively alternated to get meaningful convergence rate improvements in comparison with other BB-like gradient schemes.
On adaptive step-size selections in gradient methods / Frassoldati, Giacomo; Zanni, Luca; Zanghirati, G.. - In: PROCEEDINGS IN APPLIED MATHEMATICS AND MECHANICS. - ISSN 1617-7061. - STAMPA. - 7:(2007), pp. 1061903-1061904. (Intervento presentato al convegno Sixth International Congress on Industrial Applied Mathematics (ICIAM07) tenutosi a Zürich nel 16-20 July 2007).
On adaptive step-size selections in gradient methods
FRASSOLDATI, Giacomo;ZANNI, Luca;
2007
Abstract
In recent years several proposals for the step-size selection have largely improved the gradient methods, in the case of both constrained and unconstrained nonlinear optimization. We introduce a new step-size rule with some crucial properties. We design step-size selection strategies where the new rule and a standard Barzilai-Borwein (BB) rule can be adaptively alternated to get meaningful convergence rate improvements in comparison with other BB-like gradient schemes.
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