Cubic regularization of Newton’s method for convex problems with constraints

Yu. Nesterov

No 2006039, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper we derive effciency estimates of the regularized Newton's method as applied to constrained convex minimization problems and to variational inequalities. We study a one- step Newton's method and its multistep accelerated version, which converges on smooth convex problems as O( 1 k3 ), where k is the iteration counter. We derive also the effciency estimate of a second-order scheme for smooth variational inequalities. Its global rate of convergence is established on the level O( 1 k ).

Keywords: convex optimization; variational inequalities; Newton's method; cubic regularization; worst-case complexity; global complexity bounds. (search for similar items in EconPapers)
Date: 2006-04
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