joaquimg / COSMO.jl

COSMO: An ADMM-based solver for convex conic optimisation problems (LP, QP, SOCP, SDP). Written in Julia

Features • Installation • News • Citing • Contributing

This is a Julia implementation of the Conic operator splitting method (COSMO) solver. It can solve large convex conic optimization problems of the following form:

with decision variables x ϵ R^n, s ϵ R^m and data matrices P=P'>=0, q ϵ R^n, A ϵ R^(m×n), and b ϵ R^m. The convex set K is a composition of convex sets and cones.

For more information check the COSMO.jl Documentation.

Features

• Versatile: COSMO solves linear programs, quadratic programs, second-order cone programs and semidefinite programs
• Quad SDPs: Positive semidefinite programs with quadratic objective functions are natively supported
• Infeasibility detection: Infeasible problems are detected without a homogeneous self-dual embedding of the problem
• JuMP support: COSMO supports MathOptInterface and JuMP v0.19, which allows you to describe your problem in JuMP
• Chordal decomposition: COSMO tries to decompose large structured PSD constraints using chordal decomposition techniques. This often results in a significant speedup compared to the original problem.
• Warm starting: COSMO supports warm starting of the decision variables
• Open Source: Our code is free to use and distributed under the Apache 2.0 Licence

Installation

• COSMO can be added via the Julia package manager (type ]): pkg> add COSMO

Citing 📃

If you find COSMO useful in your project, we kindly request that you cite the following paper:

@article{garstka_2019,
  author        = {Michael Garstka and Mark Cannon and Paul Goulart},
  title         = {{COSMO}: A conic operator splitting method for convex conic problems},
  journal       = {arXiv e-prints},
  year          = {2019},
  month         = jan,
  archiveprefix = {arXiv},
  eprint        = {1901.10887},
  keywords      = {Mathematics - Optimization and Control},
  primaryclass  = {math.OC},
  url           = {https://arxiv.org/abs/1901.10887},
}

A preprint can be downloaded here.

Contributing

• Contributions are always welcome. Our style guide can be found here.
• Current issues, tasks and future ideas are listed in Issues❗. Please report any issues or bugs that you encounter.
• As an open source project we are also interested in any projects and applications that use COSMO. Please let us know!

Licence

This project is licensed under the Apache License - see the LICENSE.md file for details.