Understanding Notions of Stationarity in Nonsmooth Optimization: A Guided Tour of Various Constructions of Subdifferential for Nonsmooth Functions

You are here

Top Reasons to Join SPS Today!

1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.

Understanding Notions of Stationarity in Nonsmooth Optimization: A Guided Tour of Various Constructions of Subdifferential for Nonsmooth Functions

By: 
Jiajin Li; Anthony Man-Cho So; Wing-Kin Ma

Many contemporary applications in signal processing and machine learning give rise to structured nonconvex nonsmooth optimization problems that can often be tackled by simple iterative methods quite effectively. One of the keys to understanding such a phenomenon-and, in fact, a very difficult conundrum even for experts-lies in the study of "stationary points" of the problem in question. Unlike smooth optimization, for which the definition of a stationary point is rather standard, there are myriad definitions of stationarity in nonsmooth optimization. In this article, we provide an introduction to different stationarity concepts for several important classes of nonconvex nonsmooth functions, discuss the geometric interpretations of these concepts, and further clarify their relationships. We then demonstrate the relevance of these constructions in some representative applications and indicate how they could affect the performance of iterative methods for addressing these applications.

SPS on Twitter

  • DEADLINE EXTENDED: The 2023 IEEE International Workshop on Machine Learning for Signal Processing is now accepting… https://t.co/NLH2u19a3y
  • ONE MONTH OUT! We are celebrating the inaugural SPS Day on 2 June, honoring the date the Society was established in… https://t.co/V6Z3wKGK1O
  • The new SPS Scholarship Program welcomes applications from students interested in pursuing signal processing educat… https://t.co/0aYPMDSWDj
  • CALL FOR PAPERS: The IEEE Journal of Selected Topics in Signal Processing is now seeking submissions for a Special… https://t.co/NPCGrSjQbh
  • Test your knowledge of signal processing history with our April trivia! Our 75th anniversary celebration continues:… https://t.co/4xal7voFER

IEEE SPS Educational Resources

IEEE SPS Resource Center

IEEE SPS YouTube Channel