Article Dans Une Revue Information and Inference Année : 2023

Sharp, strong, and unique minimizers for low complexity robust recovery

Résumé

In this paper, we show the important roles of sharp minima and strong minima for robust recovery. We also obtain several characterizations of sharp minima for convex regularized optimization problems. Our characterizations are quantitative and verifiable especially for the case of decomposable norm regularized problems including sparsity, group-sparsity, and low-rank convex problems. For group-sparsity optimization problems, we show that a unique solution is a strong solution and obtain quantitative characterizations for solution uniqueness.

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hal-03989390 , version 1 (14-02-2023)

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Jalal M. Fadili, Nghia Tran T. A., Tran Trinh T. T.. Sharp, strong, and unique minimizers for low complexity robust recovery. Information and Inference, In press, 12 (3), ⟨10.1093/imaiai/iaad005⟩. ⟨hal-03989390⟩
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