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

Journal article

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 benchmark problems. Clarabel is faster than competing commercial and open-source solvers across a range of test sets with quadratic objectives, and remains competitive for problems with linear objectives even at large scale. Clarabel is currently distributed as a default solver for the Python Cvxpy optimization suite.

Authors: Goulart, PJ; Chen, Y

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Mathematical Programming Computation
• Publication date: 2026-05-21
• DOI: 10.1007/s12532-026-00320-7
• EISSN: 1867-2957
• ISSN: 1867-2949
• Language: English
• Keywords: Optimization problem; Embedding; Solver; Quadratic programming; Quadratically constrained quadratic program; Conic optimization; Range (aeronautics); Quadratic equation