587. Designing Monotone Operator Splitting Algorithms with Steering Vectors
Invited abstract in session WC-2: Systematic and computer-aided analyses VI: Systematic approaches to the analyses of proximal and higher-order methods, stream Systematic and computer-aided analyses of optimization algorithms.
Wednesday, 14:00-16:00Room: B100/7011
Authors (first author is the speaker)
| 1. | Max Nilsson
|
| Department of Automatic Control, Lund University | |
| 2. | Sebastian Banert
|
| Uni Bremen | |
| 3. | Pontus Giselsson
|
| Dept. of Automatic Control, Lund University |
Abstract
In this work, we study iterative algorithms for solving the monotone inclusion problem involving the sum of m maximally monotone operators over a Hilbert space. We take a novel approach by deriving algorithms directly from Lyapunov analysis, reversing the conventional workflow of algorithm research. Our methodology is based on iteratively simplifying a Fejér monotonic quadratic inequality, which we reformulate using an LDL^T factorization. This transforms the problem of algorithm design into an inertia eigenvalue problem, allowing us to characterize and construct provably convergent schemes. Our framework provides insights into existing resolvent-splitting methods and the underlying structure of their convergence.
Keywords
- Monotone inclusion problems
Status: accepted
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