Fast structured Jacobi-Jacobi transforms
- Award ID(s):
- 1720440
- PAR ID:
- 10167328
- Date Published:
- Journal Name:
- Mathematics of Computation
- Volume:
- 88
- Issue:
- 318
- ISSN:
- 0025-5718
- Page Range / eLocation ID:
- 1743 to 1772
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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First-order optimization algorithms are widely used today. Two standard building blocks in these algorithms are proximal operators (proximals) and gradients. Although gradients can be computed for a wide array of functions, explicit proximal formulas are known for only limited classes of functions. We provide an algorithm, HJ-Prox, for accurately approximating such proximals. This is derived from a collection of relations between proximals, Moreau envelopes, Hamilton–Jacobi (HJ) equations, heat equations, and Monte Carlo sampling. In particular, HJ-Prox smoothly approximates the Moreau envelope and its gradient. The smoothness can be adjusted to act as a denoiser. Our approach applies even when functions are accessible only by (possibly noisy) black box samples. We show that HJ-Prox is effective numerically via several examples.more » « less
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