CuClarabel: GPU Acceleration for a Conic Optimization Solver

TL;DR

CuClarabel delivers a GPU-accelerated interior-point solver for conic optimization by exploiting a mixed parallel strategy across cone types and leveraging cuDSS for direct linear solves. The Julia implementation supports a product of atomic cones, offers mixed-precision solves, and demonstrates substantial speedups over CPU-based solvers across QP, SOCP, exponential-cone, and SDP problems, including parametric and multistage settings. Key innovations include dynamic parallelism for high-dimensional SOCs, batched PSD handling, and structure-aware data layouts that maximize GPU throughput. The work highlights practical gains for large-scale conic optimization on GPUs and outlines future extensions to general SDPs, first-order hybrids, and CUDA-graph driven optimizations to further boost 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.

Figures (2)

• Figure 1: Illustration of AoS (CPU) and SoA (GPU) data structure
• Figure 2: Performance profiles for the large OPF SOCPs problem set