Abstract
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 language | English |
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Journal | Journal of Optimization Theory and Applications |
DOIs | |
State | Accepted/In press - 2023 |
Keywords
- Alternating minimization
- FISTA
- 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