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Mathematics > Optimization and Control

arXiv:2308.09224 (math)
[Submitted on 18 Aug 2023]

Title:Geometric characterizations for strong minima with applications to nuclear norm minimization problems

Authors:Jalal Fadili, Tran T. A. Nghia, Duy Nhat Phan
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Abstract:In this paper, we introduce several geometric characterizations for strong minima of optimization problems. Applying these results to nuclear norm minimization problems allows us to obtain new necessary and sufficient quantitative conditions for this important property. Our characterizations for strong minima are weaker than the Restricted Injectivity and Nondegenerate Source Condition, which are usually used to identify solution uniqueness of nuclear norm minimization problems. Consequently, we obtain the minimum (tight) bound on the number of measurements for (strong) exact recovery of low-rank matrices.
Comments: 41 pages
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)
MSC classes: 52A41, 90C25, 49J53, 49J52
Cite as: arXiv:2308.09224 [math.OC]
  (or arXiv:2308.09224v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2308.09224

Submission history

From: Duy Nhat Phan [view email]
[v1] Fri, 18 Aug 2023 00:56:58 UTC (604 KB)
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