Clarabel is an interior point numerical solver for convex optimization problems using a novel homogeneous embedding. The Clarabel package 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.

Clarabel is available in either a native Julia or a native Rust implementation. Additional language interfaces (Python, C/C++ and R) are available for the Rust version.


  • Versatile: Clarabel 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) model, Clarabel handles quadratic objective without requiring any epigraphical reformulation of its objective function. It can therefore be significantly faster than other HSDE-based solvers for problems with quadratic objective functions.
  • Infeasibility detection: Infeasible problems are detected using using a homogeneous embedding technique.
  • Arbitrary precision types: You can solve problems with any floating point precision, e.g. Float32 or Julia's BigFloat type in Julia and f32 or f64 types in Rust.
  • Open Source: Our code is available on GitHub and distributed under the Apache 2.0 License. The Julia implementation is here. The Rust implementation and Python interface is here.


The following people are involved in the development of Clarabel:

  • Paul Goulart (main development, maths and algorithms)
  • Yuwen Chen (maths and algorithms)

All contributors are affiliated with the Control Group of the Department of Engineering Science at the University of Oxford.

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Clarabel.jl and are licensed under the Apache License 2.0 (Julia) : (Rust).