On matrix approximation problems with Ky Fan \(k\) norms

DOI10.1007/BF02210386zbMath0791.65028OpenAlexW1970769818MaRDI QIDQ1315205

G. Alistair Watson

Publication date: 11 July 1994

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02210386

zbMATH Keywords

subdifferentialefficient algorithmsspectral normtrace normmatrix approximationKy Fan \(k\) norms

Mathematics Subject Classification ID

Related Items (13)

A rank-corrected procedure for matrix completion with fixed basis coefficients ⋮ Augmented Lagrangian methods for convex matrix optimization problems ⋮ Quadratic Growth Conditions for Convex Matrix Optimization Problems Associated with Spectral Functions ⋮ Subdifferential set of the joint numerical radius of a tuple of matrices ⋮ Weakly invariant norms: geometry of spheres in the space of skew-Hermitian matrices ⋮ Learning Markov Models Via Low-Rank Optimization ⋮ Orthogonality of matrices in the Ky Fan k-norms ⋮ Uniqueness in nuclear norm minimization: flatness of the nuclear norm sphere and simultaneous polarization ⋮ Birkhoff-James orthogonality and applications: a survey ⋮ DC formulations and algorithms for sparse optimization problems ⋮ Finding the Largest Low-Rank Clusters With Ky Fan $2$-$k$-Norm and $\ell_1$-Norm ⋮ On approximation problems with zero-trace matrices ⋮ Convex analysis on Cartan subspaces.

Cites Work

• Unnamed Item
• Characterization of the subdifferential of some matrix norms
• Linear best approximation using a class of polyhedral norms
• Subdifferentials, faces, and dual matrices
• SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
• On Minimizing the Maximum Eigenvalue of a Symmetric Matrix
• On the Sum of the Largest Eigenvalues of a Symmetric Matrix
• Convex Analysis

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