Back to Search
Start Over
Newton method for ℓ0-regularized optimization
- Source :
- Numerical Algorithms. 88:1541-1570
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- As a tractable approach, regularization is frequently adopted in sparse optimization. This gives rise to regularized optimization, which aims to minimize the ℓ0 norm or its continuous surrogates that characterize the sparsity. From the continuity of surrogates to the discreteness of the ℓ0 norm, the most challenging model is the ℓ0-regularized optimization. There is an impressive body of work on the development of numerical algorithms to overcome this challenge. However, most of the developed methods only ensure that either the (sub)sequence converges to a stationary point from the deterministic optimization perspective or that the distance between each iteration and any given sparse reference point is bounded by an error bound in the sense of probability. In this paper, we develop a Newton-type method for the ℓ0-regularized optimization and prove that the generated sequence converges to a stationary point globally and quadratically under the standard assumptions, theoretically explaining that our method can perform surprisingly well.
- Subjects :
- Quadratic growth
Sequence
math.OC
0103 Numerical and Computational Mathematics
Applied Mathematics
Numerical analysis
Numerical & Computational Mathematics
010103 numerical & computational mathematics
01 natural sciences
Stationary point
Regularization (mathematics)
010101 applied mathematics
symbols.namesake
Optimization and Control (math.OC)
0102 Applied Mathematics
Norm (mathematics)
Bounded function
FOS: Mathematics
symbols
Applied mathematics
0101 mathematics
Mathematics - Optimization and Control
Newton's method
0802 Computation Theory and Mathematics
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 88
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi.dedup.....0113ed43a7af29226fe9b96295fe84a8