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Quadratic regularization with cubic descent for unconstrained optimization

Ernesto G. Birgin(egbirgin***at***ime.usp.br)
J. M. Martínez(martinez***at***ime.unicamp.br)

Abstract: Cubic-regularization and trust-region methods with worst case first-order complexity $O(\varepsilon^{-3/2})$ and worst-case second-order complexity $O(\varepsilon^{-3})$ have been developed in the last few years. In this paper it is proved that the same complexities are achieved by means of a quadratic regularization method with a cubic sufficient-descent condition instead of the more usual predicted-reduction based descent. Asymptotic convergence and order of convergence results are also presented. Finally, some numerical experiments comparing the new algorithm with a well-established quadratic regularization method are shown.

Keywords: Nonlinear programming, unconstrained minimization, quadratic regularization, cubic descent, complexity.

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Technical Report MCDO271016, State University of Campinas, Campinas, SP, Brazil, 2016.

Download: [PDF]

Entry Submitted: 10/27/2016
Entry Accepted: 10/27/2016
Entry Last Modified: 10/27/2016

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