Fast algorithms for maximizing the minimum eigenvalue in fixed dimension

In the minimum eigenvalue problem, we are given a collection of vectors in Rd, and the goal is to pick a subset B to maximize the minimum eigenvalue of the matrix ∑i∈Bvivi⊤. We give a O(nO(dlog⁡(d)/ϵ2))-time randomized algorithm that finds an assignment subject to a partition constraint whose minimu...

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Vydáno v:	Operations research letters Ročník 57; s. 107186
Hlavní autoři:	Brown, Adam, Laddha, Aditi, Singh, Mohit
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier B.V 01.11.2024
Témata:	Convex optimization Minimum eigenvalue Partition matroids Convex optimization Minimum eigenvalue Partition matroids
ISSN:	0167-6377
On-line přístup:	Získat plný text
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Popis
Shrnutí:	In the minimum eigenvalue problem, we are given a collection of vectors in Rd, and the goal is to pick a subset B to maximize the minimum eigenvalue of the matrix ∑i∈Bvivi⊤. We give a O(nO(dlog⁡(d)/ϵ2))-time randomized algorithm that finds an assignment subject to a partition constraint whose minimum eigenvalue is at least (1−ϵ) times the optimum, with high probability. As a byproduct, we also get a simple algorithm for an algorithmic version of Kadison-Singer problem.
ISSN:	0167-6377
DOI:	10.1016/j.orl.2024.107186