Globally Convergent Second-order Schemes for Minimizing Twice-differentiable Functions

Geovani Nunes Grapiglia and Yurii Nesterov

No 2016028, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper, we suggest new universal second-order methods for unconstrained minimization of twice-differentiable (convex or non-convex) objective function. For the current function, these methods automatically achieve the best possible global complexity estimates among different H older classes containing the Hessian of the objective. The universal methods for functional residual and for norm of the gradient are different. For development of the latter methods, we introduced a new line-search acceptance criterion, which can be seen as a nonlinear modification of the Armijo-Goldstein condition.

Keywords: unconstrained minimization; second-order methods; H older condition; worst- case global complexity bounds (search for similar items in EconPapers)
Date: 2016-07-18
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