blegat / Clarabel.jl

Clarabel.jl: Interior-point solver for convex conic optimisation problems (LPs, QPs, SOCPs, SDPs).

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Interior Point Conic Optimization for Julia

FeaturesInstallationLicenseDocumentation

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:

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.jl Documentation (stable | dev).

Features

  • Versatile: Clarabel.jl solves linear programs (LPs), quadratic programs (QPs), second-order cone programs (SOCPs) and semidefinite programs (SDPs). Future versions will provide support for problems involving exponential and power cones.
  • Quadratic objectives: Unlike interior point solvers based on the standard homogeneous self-dual embedding (HSDE), Clarabel.jl handles quadratic objective 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 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, e.g. 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 Licence

Installation

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

Licence 🔍

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

About

Clarabel.jl: Interior-point solver for convex conic optimisation problems (LPs, QPs, SOCPs, SDPs).

License:Apache License 2.0


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