Single-Loop Algorithm for Composite Optimization
Analysis
This paper introduces and analyzes a single-loop algorithm for a complex optimization problem involving Lipschitz differentiable functions, prox-friendly functions, and compositions. It addresses a gap in existing algorithms by handling a more general class of functions, particularly non-Lipschitz functions. The paper provides complexity analysis and convergence guarantees, including stationary point identification, making it relevant for various applications where data fitting and structure induction are important.
Key Takeaways
- •Develops a single-loop algorithm for a composite optimization problem with non-Lipschitz functions.
- •Provides complexity analysis and convergence guarantees.
- •Addresses a gap in existing algorithms by handling a more general class of functions.
- •Establishes vanishing bounds on successive changes of iterates under certain conditions.
- •Shows how to construct a subsequence converging to a stationary point.
Reference
“The algorithm exhibits an iteration complexity that matches the best known complexity result for obtaining an (ε₁,ε₂,0)-stationary point when h is Lipschitz.”