Gradient flows and randomised thresholding: sparse inversion and classification. (arXiv:2203.11555v2 [math.NA] UPDATED)

Sparse inversion and classification problems are ubiquitous in modern data
science and imaging. They are often formulated as non-smooth minimisation
problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity
term and an L1/LASSO regulariser. In classification, we consider, e.g., the sum
of a data fidelity term and a non-smooth Ginzburg--Landau energy. Standard
(sub)gradient descent methods have shown to be inefficient when approaching
such problems. Splitting techniques are much more useful: here, the target
function is partitioned …

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