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

2024/05/21 by Paul J. Goulart, Goulart, Paul J., Yuwen Chen +1 · 80 citations
Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Process Optimization and Integration

paper · pdf · doi:10.48550/arxiv.2405.12762

openalex publication_date 2024/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

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