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

Nesterov, Yurii
(2006)

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  • Nesterov, YuriiUCLouvain
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Abstract
In this paper we derive efficiency 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( k13 ), where k is the iteration counter. We derive also the efficiency estimate of a second-order scheme for smooth variational inequalities. Its 1 global rate of convergence is established on the level O( k ).
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Nesterov, Y. (2006). Cubic regularization of Newton’s method for convex problems with constraints (CORE Discussion Papers 2006/39). https://hdl.handle.net/2078.5/128441