  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.
