clarabel.jl's Introduction

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:

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