Cardinality, Simplex and Proximal Operator
| Main Author: | Alberto De Marchi |
|---|---|
| Format: | info publication-workingpaper eJournal |
| Bahasa: | eng |
| Terbitan: |
, 2019
|
| Subjects: | |
| Online Access: |
https://zenodo.org/record/3334538 |
Daftar Isi:
- In this report, we consider the proximal operator for the L0 "norm", which is adopted as a sparsity-inducing penalty in e.g. compressed sensing, sparse signal representation and cardinality or cardinality-constrained optimization. Analytical expressions for the unconstrained and the nonnegative proximal point are found. Then, motivated by applications in mixed-integer optimal control, we develop a numerical method tailored for evaluating the simplex-constrained proximal operator. We present numerical investigations which demonstrate the effectiveness of the method, in terms of computation time and complexity. Also, we discuss the scaled proximal operator, arising in proximal Newton-type methods, and evaluate it via an accelerated first-order proximal method.