CuClarabel: GPU Acceleration for a Conic Optimization Solver

Abstract

We present the GPU implementation of the general-purpose interior-point solver Clarabel for convex optimization problems with conic constraints. We introduce a mixed parallel computing strategy that processes linear constraints first, then handles other conic constraints in parallel. The GPU solver currently supports linear equality and inequality constraints, second-order cones, exponential cones, power cones and positive semidefinite cones of the same dimensionality. We demonstrate that integrating a mixed parallel computing strategy with GPU-based direct linear system solvers enhances the performance of GPU-based conic solvers, surpassing their CPU-based counterparts across a wide range of conic optimization problems. We also show that employing mixed-precision linear system solvers can potentially achieve additional acceleration without compromising solution accuracy.