Name
Abstract | ||
|---|---|---|
We study the robust Rayleigh quotient optimization problem where the data matrices of the Rayleigh quotient are subject to uncertainties. We propose to solve such a problem by exploiting its characterization as a nonlinear eigenvalue problem with eigenvector nonlinearity (NEPv). For solving the NEPv, we show that a commonly used iterative method can be divergent due to a wrong ordering of the eigenvalues. Two strategies are introduced to address this issue: a spectral transformation based on nonlinear shifting and a reformulation using second-order derivatives. Numerical experiments for applications in robust generalized eigenvalue classification, robust common spatial pattern analysis, and robust linear discriminant analysis demonstrate the effectiveness of the proposed approaches. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/18M1167681 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
Rayleigh quotient,nonlinear eigenvalue problems,self-consistent-field iteration,robust optimization | Rayleigh quotient,Applied mathematics,Mathematical optimization,Nonlinear system,Matrix (mathematics),Iterative method,Robust optimization,Linear discriminant analysis,Optimization problem,Mathematics,Eigenvalues and eigenvectors | Journal |
Volume | Issue | ISSN |
40 | 5 | 1064-8275 |
Citations | PageRank | References |
3 | 0.39 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhaojun Bai | 1 | 661 | 107.69 |
| Ding Lu | 2 | 3 | 1.41 |
| Bart Vandereycken | 3 | 199 | 10.21 |