Large-Scale and Global Maximization of the Distance to Instability
| Autor: | Emre Mengi |
|---|---|
| Přispěvatelé: | Mengi, Emre (ORCID 0000-0003-0788-0066 & YÖK ID 113760), College of Sciences, Department of Department of Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
Scale (ratio) Numerical Analysis (math.NA) 010103 numerical & computational mathematics 02 engineering and technology Maximization Dynamical system 01 natural sciences Instability Matrix (mathematics) 020901 industrial engineering & automation 65F15 90C26 93D09 93D15 49K35 Eigenvalue optimization Maximin optimization Distance to instability Robust stability Subspace framework Large-scale optimization Global optimization Eigenvalue perturbation theory FOS: Mathematics Statistical physics Mathematics - Numerical Analysis 0101 mathematics Mathematics Analysis |
| Zdroj: | SIAM Journal on Matrix Analysis and Applications |
| Popis: | The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the less severe transient behavior its solution exhibits. Motivated by these issues, we consider the maximization of the distance to instability of a matrix dependent on several parameters, a nonconvex optimization problem that is likely to be nonsmooth. In the first part we propose a globally convergent algorithm when the matrix is of small size and depends on a few parameters. In the second part we deal with the problems involving large matrices. We tailor a subspace framework that reduces the size of the matrix drastically. The strength of the tailored subspace framework is proven with a global convergence result as the subspaces grow and a superlinear rate-of-convergence result with respect to the subspace dimension. 36 pages, 6 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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