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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 | dev).

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


  • 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


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


      title={Clarabel: An interior-point solver for conic programs with quadratic objectives}, 
      author={Paul J. Goulart and Yuwen Chen},

License 🔍

This project is licensed under the Apache License 2.0 - see the file for details.