A preconditioning proximal Newton method for ... - Semantic Scholar
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A preconditioning proximal Newton method for ... - Semantic Scholar
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A preconditioning proximal Newton method for nondi erentiable convex optimization 1 Liqun Qi and Xiaojun Chen School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia
We propose a proximal Newton method for solving nondi erentiable convex optimization. This method combines the generalized Newton method with Rockafellar's proximal point algorithm. At each step, the proximal point is found approximately and the regularization matrix is preconditioned to overcome inexactness of this approximation. We show that such a preconditioning is possible within some accuracy and the second-order di erentiability properties of the Moreau-Yosida regularization are invariant with respect to this preconditioning. Based upon these, superlinear convergence is established under a semismoothness condition.
1 Introduction In this paper we consider the minimization problem min ff (x);
