Accelerated regularized Newton methods for minimizing composite convex functions
(2018) , 23 pages
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- Abstract
- In this paper, we study accelerated Regularized Newton Methods for minimizing objectives formed as a sum of two functions: one is convex and twice differentiable with Hölder-continuous Hessian, and the other is a simple closed convex function. For the case in which the Hölder parameter ν ε [0, 1] is known, we propose methods that take at most O(1ε^{1/(2+ν)}) iterations to reduce the functional residual below a given precision ε > 0. For the general case, in which the ν is not known, we propose a universal method that ensures the same precision in at most O(1/ε^{2/[3(1+ν)]}) iterations.
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Citations
Nunes Grapiglia, G., & Nesterov, Y. (2018). Accelerated regularized Newton methods for minimizing composite convex functions (CORE Discussion Paper 2018/10). https://hdl.handle.net/2078.5/255580