- Quadratic regularization with cubic descent for unconstrained optimization Ernesto G. Birgin(egbirginime.usp.br) J. M. Martínez(martinezime.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: 10/27/2016Entry Accepted: 10/27/2016Entry Last Modified: 10/27/2016Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.