- On the use of third-order models with fourth-order regularization for unconstrained optimization E. G. Birgin (egbirginime.usp.br) J. L. Gardenghi (johnime.usp.br) J. M. Martínez (martinezime.unicamp.br) S. A. Santos (sandraime.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: 11/14/2017Entry Accepted: 11/14/2017Entry Last Modified: 11/14/2017Modify/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.