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Convex Optimization Primal Dual Solver

Project description

Optimus-Primal: A Lightweight primal-dual solver

optimusprimal is a light weight proximal splitting Forward Backward Primal Dual based solver for convex optimization problems. The current version supports finding the minimum of f(x) + h(A x) + p(B x) + g(x), where f, h, and p are lower semi continuous and have proximal operators, and g is differentiable. A and B are linear operators. To learn more about proximal operators and algorithms, visit proximity operator repository. We suggest that users read the tutorial “The Proximity Operator Repository. User’s guide”.


You can install optimusprimal with PyPi by running

pip install optimusprimal


Alternatively, you can install optimusprimal from GitHub by first cloning the repository

git clone
cd Optimus-Primal

and running the build script and run install tests by

pytest --black optimusprimal/tests/


After installing optimusprimal one can e.g. perform an constrained proximal primal dual reconstruction by

import numpy as np
import optimusprimal.primal_dual as primal_dual
import optimusprimal.linear_operators as linear_ops
import optimusprimal.prox_operators as prox_ops

options = {'tol': 1e-5, 'iter': 5000, 'update_iter': 50, 'record_iters': False}

# Load some data
y = np.load('Some observed signal y')                                 # Load a file of observed data.
epsilon = sigma * np.sqrt(y.size + 2 np.sqrt(y.size))                 # where sigma is your noise std.

# Define a forward model i.e. y = M(x) + n
M = np.ones_like(y)                                                   # Here M = Identity for simplicity.
p = prox_ops.l2_ball(epsilon, y, linear_ops.diag_matrix_operator(M))  # Create a l2-ball data-fidelity.

# Define a regularisation i.e. ||W(x)||_1
wav = ['db1', 'db3', 'db4']                                           # Select some wavelet dictionaries.
psi = linear_operators.dictionary(wav, levels=6, y.shape)             # Define multi-dictionary wavelets.
h = prox_ops.l1_norm(gamma=1, psi)                                    # Create an l1-norm regulariser.

# Recover an estiamte i.e. x_est = min[h(x)] s.t. p(x) <= epsilon
x_est, = primal_dual.FBPD(y, options, None, None, h, p, None)         # Recover an estimate of x.


optimusprimal is released under the GPL-3 license (see LICENSE.txt), subject to the non-commercial use condition.

Copyright (C) 2021 Luke Pratley & contributors

This program is released under the GPL-3 license (see LICENSE.txt),
subject to a non-commercial use condition (see LICENSE_EXT.txt).

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of

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