Interior Point Conic Optimization for Julia
__Clarabel.jl__ is a Julia implementation of an interior point numerical solver for convex optimization problems using a novel homogeneous embedding. Clarabel.jl solves the following problem:
$$
\begin{array}{r}
\text{minimize} & \frac{1}{2}x^T P x + q^T x\\\\[2ex]
\text{subject to} & Ax + s = b \\\\[1ex]
& s \in \mathcal{K}
\end{array}
$$
with decision variables
$x \in \mathbb{R}^n$,
$s \in \mathbb{R}^m$
and data matrices
$P=P^\top \succeq 0$,
$q \in \mathbb{R}^n$,
$A \in \mathbb{R}^{m \times n}$, and
$b \in \mathbb{R}^m$.
The convex set $\mathcal{K}$ is a composition of convex cones.
__For more information see the Clarabel Documentation ([stable](https://oxfordcontrol.github.io/ClarabelDocs/stable) | [dev](https://oxfordcontrol.github.io/ClarabelDocs/dev)).__
Clarabel is also available in a Rust implementation with additional language interfaces. See [here](https://github.com/oxfordcontrol/Clarabel.rs).
## Features
* __Versatile__: Clarabel.jl solves linear programs (LPs), quadratic programs (QPs), second-order cone programs (SOCPs) and semidefinite programs (SDPs). It also solves problems with exponential, power cone and generalized power cone constraints.
* __Quadratic objectives__: Unlike interior point solvers based on the standard homogeneous self-dual embedding (HSDE), Clarabel.jl handles quadratic objectives without requiring any epigraphical reformulation of the objective. It can therefore be significantly faster than other HSDE-based solvers for problems with quadratic objective functions.
* __Infeasibility detection__: Infeasible problems are detected using a homogeneous embedding technique.
* __JuMP / Convex.jl support__: We provide an interface to [MathOptInterface](https://jump.dev/JuMP.jl/stable/moi/) (MOI), which allows you to describe your problem in [JuMP](https://github.com/jump-dev/JuMP.jl) and [Convex.jl](https://github.com/jump-dev/Convex.jl).
* __Arbitrary precision types__: You can solve problems with any floating point precision, for example, Float32 or Julia's BigFloat type, using either the native interface, or via MathOptInterface / Convex.jl.
* __Open Source__: Our code is available on [GitHub](https://github.com/oxfordcontrol/Clarabel.jl) and distributed under the Apache 2.0 License
## Installation
- __Clarabel.jl__ can be added via the Julia package manager (type `]`): `pkg> add Clarabel`
## Citing
```
@misc{Clarabel_2024,
title={Clarabel: An interior-point solver for conic programs with quadratic objectives},
author={Paul J. Goulart and Yuwen Chen},
year={2024},
eprint={2405.12762},
archivePrefix={arXiv},
primaryClass={math.OC}
}
```
## License 🔍
This project is licensed under the Apache License 2.0 - see the [LICENSE.md](https://github.com/oxfordcontrol/Clarabel.jl/blob/main/LICENSE.md) file for details.