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arXiv · 2609.06238

Isolated calmness of regularized linear inverse problems

Tran T. A. Nghia·Huy N. Pham·Nghia V. Vo·Khoa V. H. Vu
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Abstract

This paper studies the isolated calmness property of solution mappings arising from convex regularized linear inverse problems. We mainly establish a tangent-cone characterization of this property. For convex piecewise linear-quadratic regularizers, the isolated calmness coincides with the solution uniqueness, leading to simple verification procedures. In particular, for analysis sparsity regularization, our condition can be verified by linear programming.

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Tran T. A. Nghia, Huy N. Pham, Nghia V. Vo, Khoa V. H. Vu. 2026-09-05. Isolated calmness of regularized linear inverse problems. https://arxiv.org/abs/2609.06238

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