CuClarabel: GPU Acceleration for a Conic Optimization Solver

TL;DR

This paper introduces CuClarabel, a GPU-accelerated interior-point solver for convex conic optimization, utilizing a mixed parallel computing strategy and mixed-precision linear solvers to significantly improve performance over CPU implementations.

Contribution

The paper presents a novel GPU implementation of Clarabel with a mixed parallel computing approach and mixed-precision solvers, enhancing efficiency for various conic optimization problems.

Findings

GPU solver outperforms CPU-based solvers across many problems.

Mixed-precision linear solvers can accelerate computation without losing accuracy.

Parallel processing of different conic constraints improves solver performance.

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.