scsprox

scsprox creates fast proximal operators from CVXPY Problem objects.

scsprox uses CVXPY to form the proximal operator problem and translate it to the SCS conic input format. This translation is performed only once during the Prox object initialization to save time. scsprox uses CySCS for matrix-factorization-caching and warm-starting to reduce solve times over many repeated solves, as occurs, for example, within the alternating-direction method of multipliers (ADMM) algorithm.

Please also see the tutorial Jupyter notebook.

Installation

• Clone this repository.
• Inside the repository, run python setup.py install.
• Optionally, run tests with py.test --pyargs scsprox.

Basic Usage

The Prox object

from scsprox import Prox

creates a fast proximal operator from any cvxpy.Problem and a dictionary whose values are cvxpy.Variable objects.

import numpy as np
import cxvpy as cp

m, n = 200, 100
A = np.random.randn(m,n)
b = np.random.randn(m)
x = cp.Variable(n)

prob = cp.Problem(cp.Minimize(cp.norm(A*x - b)))

xvars = {'x': x}
prox = Prox(prob, xvars)

The Prox object comes with a Prox.do(x0, rho) method which computes the prox on the input dictionary x0, whose keys must match the dictionary that the Prox object was created with.

x0 = {'x': np.zeros(n)}
rho = 1.0
x1 = prox.do(x0, rho)

Prox.info

Prox.info returns a dictionary with status information:

• info['status'] is the SCS solver status string, usually Solved or Solved/Inaccurate
• info['iter'] is the number of SCS iterations performed during the most recent evaluation of Prox.do
• info['setup_time'] is the SCS setup time in seconds, which includes the matrix factorization which is reused across calls to Prox.do
• info['solve_time'] is the SCS solve time in seconds corresponding to the most recent call to Prox.do

Settings

CySCS settings can be passed as keyword arguments do the Prox constructor or the Prox.do method. For example:

• verbose=True turns on status information printing during initialization and solves
• eps=1e-5 changes the SCS solver tolerance to 1e-5
• max_iters=400 sets the maximum number of SCS iterations to 400

Changes in settings persist across calls to Prox.do.

Warm-starting

The Prox object automatically warm-starts the solve for a call to Prox.do with the solution from the previous call. This saves time when successive calls are related, as often happens in ADMM.

You can reset the warm-start variable to 0 (where 0 is the appropriate vector size for each variable) by calling Prox.reset_warm_start().

Zero Element

The Prox object is aware of the sizes of its prox variables, and so passing x0 to Prox.do is optional. If omitted, x0=None, or x0={}, Prox will perform the prox on the appropriately-sized zero element, which can be seen by the user by calling Prox.zero_elem.

Prox.zero_elem will return a dict keyed by the variable names, with either numpy.array or float (scalar) values.

x0 Datatypes

The input x0 to Prox.do must be a dictionary whose values are either numpy.array or float objects.

Workspace

The Prox object wraps a cyscs.Workspace object, which advanced users can access through the Prox._work attribute.