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

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.