- Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models E. G. Birgin (ebirginime.isp.br) J.L. Gardenghi (johnime.isp.br) J.M. Martinez (martinezime.unicamp.br) S.A. Santos (dandraime.unicamp.br) Ph. L. Toint (philippe.tointunamur.be) Abstract: The worst-case evaluation complexity for smooth (possibly nonconvex) unconstrained optimization is considered. It is shown that, if one is willing to use derivatives of the objective function up to order $p$ (for $p\geq 1$) and to assume Lipschitz continuity of the $p$-th derivative, then an $\epsilon$-approximate first-order critical point can be computed in at most $O(\epsilon^{-(p+1)/p})$ evaluations of the problem's objective function and its derivatives. This generalizes and subsumes results known for $p=1$ and $p=2$. Keywords: Nonlinear optimization, complexity, regularization methods Category 1: Nonlinear Optimization (Unconstrained Optimization ) Citation: Report naXys-05-2015, University of Namur, Namur, Belgium Download: [PDF]Entry Submitted: 06/21/2015Entry Accepted: 06/21/2015Entry Last Modified: 07/10/2015Modify/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.