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
Safeguarded acceleration: robust and faster convergence to higher precision using COSMOAccelerators
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, for example, QDLDL, Pardiso, Conjugate Gradient and MINRES
Arbitrary precision types: You can solve problems with any floating point precision.
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:

@Article{Garstka_2021,
  author  = {Michael Garstka and Mark Cannon and Paul Goulart},
  journal = {Journal of Optimization Theory and Applications},
  title   = {{COSMO}: A Conic Operator Splitting Method for Convex Conic Problems},
  volume  = {190},
  number  = {3},
  pages   = {779--810},
  year    = {2021},
  publisher = {Springer},
  doi     = {10.1007/s10957-021-01896-x},
  url     = {https://doi.org/10.1007/s10957-021-01896-x}
}

The article is available under Open Access 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 by opening a GitHub issue.

Python - Interface

COSMO can also be called from Python. Take a look at: cosmo-python

Licence 🔍

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