A coordinate gradient descent method for nonsmooth nonseparable minimization

Z.J. Bai, M.K. Ng, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function. We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function. Under a local Lipschitzian error bound assumption, we show that the algorithm possesses global and local linear convergence properties. We also give some numerical tests (including image recovery examples) to illustrate the efficiency of the proposed method.
Original languageEnglish
Pages (from-to)377-402
Number of pages26
JournalNumerical mathematics : theory, methods and applications
Volume2
Issue number4
DOIs
Publication statusPublished - 2009

Keywords

  • Coordinate descent
  • Global convergence
  • Linear convergence rate

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Control and Optimization
  • Modelling and Simulation

Cite this