Roman Polyak | George Mason Univefrsity
address: SEOR, George Mason University, Fairfax, VA 22030
phone: 703.993.1685 | email: rpolyak@gmu.edu
website: http://mason.gmu.edu/~rpolyak/


Title: Regularized Newton's Method for Unconstrained Optimization

Abstract
We introduced the regularized Newton's method (RNM) for unconstrained convex optimization. For any convex function with bounded optimal set the rnm generates a sequence that converges to the optimal set from any starting point. The RNM requires neither strong convexity nor smoothness properties in the entire space. If the function is strongly convex and its Hessian satisfies Lipschitz condition in the neighborhood of the solution then the RNM sequence converges to the unique solution with quadratic rate. We characterized the neighborhood of the solution from which the quadratic rate occurs through the convexity constant of the function and Lipschitz constant of the Hessian.