PreprintCC0arXiv
Isolated calmness of regularized linear inverse problems
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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BibTeX
@misc{nghia2026isolated,
title = {{Isolated calmness of regularized linear inverse problems}},
author = {Tran T. A. Nghia and Huy N. Pham and Nghia V. Vo and Khoa V. H. Vu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06238},
eprint = {2609.06238},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06238},
note = {CC0},
}
RIS
TY - UNPB
TI - Isolated calmness of regularized linear inverse problems
AU - Tran T. A. Nghia
AU - Huy N. Pham
AU - Nghia V. Vo
AU - Khoa V. H. Vu
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.06238
UR - https://arxiv.org/abs/2609.06238
AB - 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.
ER -