# Clarabel: An interior-point solver for conic programs with quadratic objectives

arXiv: https://arxiv.org/abs/2405.12762 · HTML: https://mlsanity.com/paper/2405.12762/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2024.

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## Abstract (arXiv)

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.