Abstract
Matrix variables are ubiquitous in modern optimization, in part because variational properties of useful matrix functions often expedite standard optimization algorithms. Convexity is one important such property: permutation-invariant convex functions of the eigenvalues of a symmetric matrix are convex, leading to the wide applicability of semidefinite programming algorithms. We prove the analogous result for the property of "identifiability," a notion central to many activeset- type optimization algorithms. © 2014 Society for Industrial and Applied Mathematics.
Original language | English |
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Pages (from-to) | 580-598 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 35 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Keywords
- Duality
- Eigenvalues
- Identifiable set
- Partial smoothness
- Polyhedra
- Symmetric matrix