COSMO: An ADMM-based solver for convex conic optimisation problems (LP, QP, SOCP, SDP, ExpCP, PowCP). Implemented in Julia
Author oxfordcontrol
108 Stars
Updated Last
10 Months Ago
Started In
January 2018


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).


  • 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
  • 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.


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


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

  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           = {},
  archiveprefix = {arXiv},
  keywords      = {Mathematics - Optimization and Control},
  primaryclass  = {math.OC},

A preprint can be downloaded here.


  • 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 file for details.

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