Work

Proximal Newton-Type Methods for Minimizing Composite Functions

Year: 2014

Type: article

Abstract: We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing smooth functions, even when search directions are computed inexactly. Many popular methods tailored to problems arising in bioinformatics, signal processing, and statistical learning are special cases of proximal Newton-type methods, and our analysis yields new convergence results for some of these methods.

Source: SIAM Journal on Optimization

DOI: 10.1137/130921428

Authors: Jason D. Lee, Yuekai Sun, Michael A. Saunders

Institution: Stanford University

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green