Proximal Newton-type methods for minimizing composite functions

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

Research output: Contribution to journalArticle

77 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1420-1443
Number of pages24
JournalSIAM Journal on Optimization
Volume24
Issue number3
DOIs
StatePublished - Jan 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science

Keywords

  • Convex optimization
  • Nonsmooth optimization
  • Proximal mapping

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