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ROBUST RAYLEIGH QUOTIENT MINIMIZATION AND NONLINEAR EIGENVALUE PROBLEMS
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DOI：10.1137/18M1167681.png)
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Abstract
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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.
Keywords:
Rayleigh quotient
nonlinear eigenvalue problems
self-consistent-field iteration
robust optimization
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