Proximal Newton-type methods for minimizing composite functions
Jason D. Lee11 1 J. Lee and Y. Sun contributed equally to this work. 22 2 Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California. Yuekai Sun11 1 J. Lee and Y. Sun contributed equally to this work. 22 2 Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California. Michael A. Saunders33 3 Department of Management Science and Engineering, Stanford University, Stanford, California.
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.
原文 arXiv:1206.1623;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1206.1623v13