Proximal algorithms /
This monograph is about a class of optimization algorithms called proximal algorithms. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-sca...
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[Hanover, Massachusetts] :
Now Publishers,
2014
|
| Series: | Foundations and trends in optimization ;
volume 1, issue 3, pages 127-239 |
| Subjects: |
Table of Contents:
- 1. Introduction
- 1.1 Definition
- 1.2 Interpretations
- 1.3 Proximal algorithms
- 1.4 What this paper is about
- 1.5 Related work
- 1.6 Outline
- 2. Properties
- 2.1 Separable sum
- 2.2 Basic operations
- 2.3 Fixed points
- 2.4 Proximal average
- 2.5 Moreau decomposition
- 3. Interpretations
- 3.1 Moreau-Yosida regularization
- 3.2 Resolvent of subdifferential operator
- 3.3 Modified gradient step
- 3.4 Trust region problem
- 3.5 Notes and references
- 4. Proximal algorithms
- 4.1 Proximal minimization
- 4.2 Proximal gradient method
- 4.3 Accelerated proximal gradient method
- 4.4 Alternating direction method of multipliers
- 4.5 Notes and references
- 5. Parallel and distributed algorithms
- 5.1 Problem structure
- 5.2 Consensus
- 5.3 Exchange
- 5.4 Allocation
- 5.5 Notes and references
- 6. Evaluating proximal operators
- 6.1 Generic methods
- 6.2 Polyhedra
- 6.3 Cones
- 6.4 Pointwise maximum and supremum
- 6.5 Norms and norm balls
- 6.6 Sublevel set and epigraph
- 6.7 Matrix functions
- 6.8 Notes and references
- 7. Examples and applications
- 7.1 Lasso
- 7.2 Matrix decomposition
- 7.3 Multi-period portfolio optimization
- 7.4 Stochastic optimization
- 7.5 Robust and risk-averse optimization
- 7.6 Stochastic control
- 8. Conclusions
- References