Optimization Algorithms on Matrix Manifolds¶
Absil, P. -., Mahony, R., & Sepulchre, R. (2008). Optimization Algorithms on Matrix Manifolds. Princeton University Press.
Cited by¶
1 citation across 1 artifact.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Manifold
- In optimisation the constraint set is often itself a manifold — the sphere, the Stiefel manifold, the positive-definite cone — and respecting its local-flat structure preserves convergence.
This sourceDevelops optimization on constraint manifolds (the sphere, Stiefel and Grassmann manifolds, the positive-definite cone), respecting local-flat structure to preserve convergence.
Supported in partVerified against the work's full text
The publisher's description grounds optimization on manifold-structured search spaces but does not name the sphere, Stiefel or PD cone, nor convergence from respecting local-flat structure.
“Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms.”
- In optimisation the constraint set is often itself a manifold — the sphere, the Stiefel manifold, the positive-definite cone — and respecting its local-flat structure preserves convergence.
Verification¶
Does it exist? Not checked yet. This entry carries no identifier to resolve. It was extracted from the citation as written in the article, normalized, and deduplicated against the rest of the registry.
Does it back the claim? Read against the text for 1 of 1 citation: 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:1e5d7c5b0ff8 · see in the full table