Clarabel: An interior-point solver for conic programs with quadratic objectives
- 1University of Oxford, Oxford, UK
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 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.
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BibTeX
@article{goulart2026clarabel,
title = {{Clarabel: An interior-point solver for conic programs with quadratic objectives}},
author = {Paul J. Goulart and Yuwen Chen},
journal = {Mathematical Programming Computation},
year = {2026},
month = may,
doi = {10.1007/s12532-026-00320-7},
url = {https://doi.org/10.1007/s12532-026-00320-7},
note = {CC BY},
}
RIS
TY - JOUR
TI - Clarabel: An interior-point solver for conic programs with quadratic objectives
AU - Paul J. Goulart
AU - Yuwen Chen
PY - 2026
DA - 2026/05/21
JO - Mathematical Programming Computation
DO - 10.1007/s12532-026-00320-7
UR - https://doi.org/10.1007/s12532-026-00320-7
AB - 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.
SN - 1867-2949
SN - 1867-2957
ER -