Separable cubic modeling and a trust-region strategy for unconstrained minimization with impact in global optimization

J. Martínez () and M. Raydan ()

Journal of Global Optimization, 2015, vol. 63, issue 2, 319-342

Abstract: A separable cubic model, for smooth unconstrained minimization, is proposed and evaluated. The cubic model uses some novel secant-type choices for the parameters in the cubic terms. A suitable hard-case-free trust-region strategy that takes advantage of the separable cubic modeling is also presented. For the convergence analysis of our specialized trust region strategy we present as a general framework a model $$q$$ q -order trust region algorithm with variable metric and we prove its convergence to $$q$$ q -stationary points. Some preliminary numerical examples are also presented to illustrate the tendency of the specialized trust region algorithm, when combined with our cubic modeling, to escape from local minimizers. Copyright Springer Science+Business Media New York 2015

Keywords: Smooth unconstrained minimization; Cubic modeling; Trust-region strategies; Newton-type methods (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-015-0278-3

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