# Interior Point Conic Optimization for Julia

Features • Installation • License • Documentation

**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 | dev).**

Clarabel is also available in a Rust implementation with additional language interfaces. See here.

## 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 (MOI), which allows you to describe your problem in JuMP and 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 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 file for details.