First- and second-order epi-differentiability in eigenvalue optimization

DOI10.1006/jmaa.1999.6320zbMath1016.90061OpenAlexW2035258331MaRDI QIDQ1301867

Mounir Torki

Publication date: 12 September 1999

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1999.6320

zbMATH Keywords

sensitivityoptimality conditionsspectral functionsepi-differentiabilityparameterized real symmetric matrices

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Optimality conditions and duality in mathematical programming (90C46) Sensitivity, stability, parametric optimization (90C31) Nonsmooth analysis (49J52)

Related Items (10)

The bundle scheme for solving arbitrary eigenvalue optimizations ⋮ Analysis of Symmetric Matrix Valued Functions ⋮ The space decomposition method for the sum of nonlinear convex maximum eigenvalues and its applications ⋮ Some New Methods for Generating Convex Functions ⋮ Twice Epi-Differentiability of Extended-Real-Valued Functions with Applications in Composite Optimization ⋮ Second-order conditions for existence of augmented Lagrange multipliers for eigenvalue composite optimization problems ⋮ Quadratic expansions of spectral functions ⋮ A Decomposition Algorithm for the Sums of the Largest Eigenvalues ⋮ Spectral bundle methods for non-convex maximum eigenvalue functions: second-order methods ⋮ Second-order directional derivatives of spectral functions

Cites Work

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• Second Derivatives for Optimizing Eigenvalues of Symmetric Matrices
• On Eigenvalue Optimization
• Second-order directional derivatives of all eigenvalues of a symmetric matrix

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