21. Solving sequences of parametrized Lyapunov equations for efficient simulation of parameter influence
Invited abstract in session TB-4: Modeling, Simulation and Optimization, stream Large scale optimization and applications.
Thursday, 10:00 - 11:30Room: C105
Authors (first author is the speaker)
| 1. | Zoran Tomljanovic
|
| School of Applied Mathematics and Informatics J. J. Strossmayer University of Osijek |
Abstract
We consider a sequence of parametrized Lyapunov equations that can be encountered in many application settings. Repeated solutions of such equations are often intermediate steps of an overall procedure whose main goal is analyzing parameter influence or parameter optimization.
We are interested in addressing problems where the parameter dependency of the coefficient matrix is encoded as a low-rank modification to a seed, fixed matrix. We propose two novel numerical procedures that fully exploit such a common structure. The first one builds upon recycling Krylov techniques, and it is well-suited for small dimensional problems as it makes use of dense numerical linear algebra tools. The second algorithm can instead address large-scale problems by relying on state-of-the-art projection techniques based on the extended Krylov subspace.
We show the efficiency of the new algorithms on several problems arising in the study of damped vibrational systems and the analyses of output synchronization problems for multi-agent systems.
This is joint work with Davide Palitta, Ivica Nakic and Jens Saak.
Keywords
- Linear and nonlinear optimization
- Optimal control and applications
- Optimization in industry, business and finance
Status: accepted
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