Nested Alternating Minimization with FISTA for Non-convex and Non-smooth Optimization Problems

Research output: Contribution to journalArticlepeer-review


Motivated by a recent framework for proving global convergence to critical points of nested alternating minimization algorithms, which was proposed for the case of smooth subproblems, we first show here that non-smooth subproblems can also be handled within this framework. Specifically, we present a novel analysis of an optimization scheme that utilizes the FISTA method as a nested algorithm. We establish the global convergence of this nested scheme to critical points of non-convex and non-smooth optimization problems. In addition, we propose a hybrid framework that allows to implement FISTA when applicable, while still maintaining the global convergence result. The power of nested algorithms using FISTA in the non-convex and non-smooth setting is illustrated with some numerical experiments that show their superiority over existing methods.

Original languageEnglish
JournalJournal of Optimization Theory and Applications
StateAccepted/In press - 2023


  • Alternating minimization
  • Global convergence
  • Nested algorithms
  • Non-convex and non-smooth optimization

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


Dive into the research topics of 'Nested Alternating Minimization with FISTA for Non-convex and Non-smooth Optimization Problems'. Together they form a unique fingerprint.

Cite this