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2401. Linear Convergence of Fixed-Point Iteration of Averaged Operators via a Generic Error-Bound Condition
Invited abstract in session WB-38: Convex and conic optimization, stream Conic Optimization: Theory, Algorithms, and Applications.
Wednesday, 10:30-12:00Room: 34 (building: 306)
Authors (first author is the speaker)
| 1. | Kira van Treek
|
| Econometrics and Operations Research, Tilburg University | |
| 2. | Javier Peña
|
| Carnegie Mellon University | |
| 3. | Juan Vera
|
| Econometrics and Operations Research, Tilburg University | |
| 4. | Luis Zuluaga
|
| Lehigh University |
Abstract
Several optimization algorithms, including the ADMM and Douglas-Rachford algorithm (DR), can be cast as the fixed-point iteration (FPI) of an averaged operator. However, the convergence of these algorithms is slow in general (within sublinear regime). We show linear convergence of the FPI of averaged operators by leveraging an error-bound condition on the operator. Our work captures several existing results on the linear convergence of the ADMM and DR under stronger assumptions. As a byproduct of our method, we bound the rate of convergence of the DR applied to linear and quadratic optimization problems.
Keywords
- Algorithms
- Continuous Optimization
- Mathematical Programming
Status: accepted
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