Clarabel: An interior-point solver for conic programs with quadratic objectives
Paul J. Goulart, Yuwen Chen
TL;DR
Clarabel introduces a general-purpose interior-point solver for convex conic programs with quadratic objectives, grounded in a homogeneous self-dual embedding specialized for such problems. It supports both symmetric and nonsymmetric cones and leverages chordal decomposition for large SDPs, with robust initialization, scalable LDL^T factorization, and flexible scaling strategies. Across extensive benchmarks, Clarabel consistently outperforms state-of-the-art solvers, especially on quadratic-objective problems and sparse SDPs, and is integrated into CVXPY via Python. The solver is released as open-source in Rust and Julia, enabling broad adoption and future extensions in conic optimization tasks.
Abstract
We present a general-purpose interior-point solver for convex optimization problems with conic constraints. Our method is based on a homogeneous embedding method originally developed for general monotone complementarity problems and more recently applied to operator splitting methods, and here specialized to an interior-point method for problems with quadratic objectives. We allow for a variety of standard symmetric and non-symmetric cones, and provide support for chordal decomposition methods in the case of semidefinite cones. We describe the implementation of this method in the open-source solver Clarabel, and provide a detailed numerical evaluation of its performance versus several state-of-the-art solvers on a wide range of standard benchmarks problems. Clarabel is faster and more robust than competing commercial and open-source solvers across a range of test sets, with a particularly large performance advantage for problems with quadratic objectives. Clarabel is currently distributed as a standard solver for the Python CVXPY optimization suite.