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 take a look at the COSMO.jl Documentation (stable | dev).

Features

• Versatile: COSMO solves linear programs, quadratic programs, second-order cone programs, semidefinite programs and problems involving exponential and power cones

• 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 / Convex.jl support: We provide an interface to MathOptInterface (MOI), which allows you to describe your problem in JuMP and Convex.jl.

• Warm starting: COSMO supports warm starting of the decision variables

• Custom sets and linear solver: Customize COSMO's components by defining your own convex constraint sets and by choosing from a number of direct and indirect linear system solvers, e.g. QDLDL, Pardiso, Conjugate Gradient and MINRES

• Open Source: Our code is free to use and distributed under the Apache 2.0 Licence

• 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.

• Smart clique merging: After an initial decomposition of a structured SDP, COSMO recombines overlapping cliques/blocks to speed up the algorithm.

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:

@InProceedings{garstka_2019,
  author        = {Michael Garstka and Mark Cannon and Paul Goulart},
  title         = {{COSMO}: A conic operator splitting method for large convex problems},
  booktitle     = {European Control Conference},
  year          = {2019},
  location      = {Naples, Italy},
  doi            = {10.23919/ECC.2019.8796161},
  eprint        = {1901.10887},
  url           = {https://arxiv.org/abs/1901.10887},
  archiveprefix = {arXiv},
  keywords      = {Mathematics - Optimization and Control},
  primaryclass  = {math.OC},
}

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.