Interior point solver for general convex conic optimization problems
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Updated Last
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Started In
July 2018

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Hypatia is a highly-customizable open source interior point solver for generic conic optimization problems, written in Julia. It is licensed under the MIT License (see LICENSE).

For more information on Hypatia, please see:

and preprints of our papers:

and corresponding raw results CSV files generated by our run scripts in the benchmarks folder.


To use Hypatia, install Julia, then at the Julia REPL, type:

using Hypatia
using Pkg

Hypatia is an experimental solver and a work in progress, and may not run with older releases of Julia. Default options/parameters are not well-tuned, so we encourage you to experiment with these.


Hypatia can be accessed through a low-level native Julia interface or through open-source modeling tools such as JuMP and Convex.jl. The native interface is more expressive, allowing Hypatia to solve conic models expressed with generic real floating point types and structured matrices or linear operators, for example. However, it is typically sufficient and more convenient to use JuMP.

Using JuMP, we can model a simple D-optimal experiment design problem and call Hypatia:

using LinearAlgebra
using JuMP
using Hypatia

# setup JuMP model
opt = Hypatia.Optimizer(verbose = false)
model = Model(() -> opt)
@variable(model, x[1:3] >= 0)
@constraint(model, sum(x) == 5)
@variable(model, hypo)
@objective(model, Max, hypo)
V = rand(2, 3)
Q = V * diagm(x) * V'
aff = vcat(hypo, [Q[i, j] for i in 1:2 for j in 1:i]...)
@constraint(model, aff in MOI.RootDetConeTriangle(2))

# solve and query solution

See our D-optimal design example for more information and references.

Many more examples using the native interface or JuMP can be found in the examples folder.


Comments, questions, suggestions, and improvements/extensions to the code or documentation are welcomed. Please reach out on Discourse, or submit an issue or contribute a PR on our Github repo. If contributing code, try to maintain consistent style and add docstrings or comments for clarity. New examples are welcomed and should be implemented similarly to the existing examples.


This work has been partially funded by the National Science Foundation under grant OAC-1835443 and the Office of Naval Research under grant N00014-18-1-2079.

Citing Hypatia

If you find Hypatia solver useful, please cite our solver paper:

    title={Solving natural conic formulations with {H}ypatia.jl},
    author={Chris Coey and Lea Kapelevich and Juan Pablo Vielma},
    journal={INFORMS Journal on Computing},

If you find aspects of Hypatia's IPM implementation useful, please cite our algorithm paper:

    title={Performance enhancements for a generic conic interior point algorithm},
    author={Chris Coey and Lea Kapelevich and Juan Pablo Vielma},
    journal={Mathematical Programming Computation},