Numerical Optimization of Eigenvalues of Hermitian Matrix Functions

DOI10.1137/130933472zbMath1307.65043arXiv1109.2080OpenAlexW2037064199MaRDI QIDQ2923367

E. Alper Yıldırım, Emre Mengi, Mustafa Kiliç

Publication date: 15 October 2014

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.2080

zbMATH Keywords

algorithmglobal optimizationglobal convergencenumerical examplesnumerical radiusperturbation of eigenvaluesdistance to uncontrollabilityanalytic and Hermitian matrix-valued functionHermitian eigenvalues

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Nonconvex programming, global optimization (90C26) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (20)

Generalized derivatives of eigenvalues of a symmetric matrix ⋮ Derivatives of symplectic eigenvalues and a Lidskii type theorem ⋮ Robust stability optimization for linear delay systems in a probabilistic framework ⋮ Model Order Reduction in Contour Integral Methods for Parametric PDEs ⋮ Large-Scale Computation of $\mathcal{L}_\infty$-Norms by a Greedy Subspace Method ⋮ A Support Function Based Algorithm for Optimization with Eigenvalue Constraints ⋮ Matrix polynomials with specified eigenvalues ⋮ Nonlinear Eigenvector Methods for Convex Minimization over the Numerical Range ⋮ Large-Scale and Global Maximization of the Distance to Instability ⋮ Approximation of stability radii for large-scale dissipative Hamiltonian systems ⋮ Black-box learning of multigrid parameters ⋮ Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations ⋮ Subspace Acceleration for Large-Scale Parameter-Dependent Hermitian Eigenproblems ⋮ Krylov subspace methods for discrete-time algebraic Riccati equations ⋮ Approximate residual-minimizing shift parameters for the low-rank ADI iteration ⋮ Nonsmooth Optimization Method for H∞ Output Feedback Control ⋮ An unconstrained global optimization framework for real symmetric eigenvalue problems ⋮ A Subspace Framework for ${\mathcal H}_\infty$-Norm Minimization ⋮ Differential Equations for Real-Structured Defectivity Measures ⋮ A Subspace Method for Large-Scale Eigenvalue Optimization

Uses Software

• Matlab
• CTDSX

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