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On the use of third-order models with fourth-order regularization for unconstrained optimization

E. G. Birgin (egbirgin***at***ime.usp.br)
J. L. Gardenghi (john***at***ime.usp.br)
J. M. Martínez (martinez***at***ime.unicamp.br)
S. A. Santos (sandra***at***ime.unicamp.br)

Abstract: In a recent paper, it was shown that, for the smooth unconstrained optimization problem, worst-case evaluation complexity $O(\epsilon^{-(p+1)/p})$ may be obtained by means of algorithms that employ sequential approximate minimizations of p-th order Taylor models plus (p + 1)-th order regularization terms. The aforementioned result, which assumes Lipschitz continuity of the p-th partial derivatives, generalizes the case p = 2, known since 2006, which has already motivated efficient implementations. The present paper addresses the issue of defining a reliable algorithm for the case p = 3. With that purpose, we propose a specific algorithm and we show numerical experiments.

Keywords: unconstrained minimization, third-order models, regularization, complexity

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: 2017

Download: [PDF]

Entry Submitted: 11/14/2017
Entry Accepted: 11/14/2017
Entry Last Modified: 11/14/2017

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