Regularized Newton Method for Optimizing Strongly Convex Functions

Student: Doikov Nikita

Supervisor: Yury Maximov

Educational Programme: Mathematical Methods of Optimization and Stochastics (Master)

Year of Graduation: 2017

In this work we study upper iteration complexity bound of the cubic regularized Newton method for optimizing strongly convex functions with Lipschitz-continuous gradient and Hessian. Linear rate of convergence is shown for the method with specially developed line-search strategy for each iteration. Global complexity bound is given, the number of iterations for optimization with eps accuracy is O(L/a log 1/eps), where 'a' and 'L' are parameters of strong convexity and Lipschitz-continuity of gradient, respectively. Local rate of convergence is quadratic for the proposed optimization scheme.

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