QOCO-GPU: A Quadratic Objective Conic Optimizer with GPU Acceleration

TL;DR

This paper introduces a GPU-accelerated backend for the QOCO solver, significantly speeding up quadratic and SOCP problem solving using CUDA and a modular design.

Contribution

It develops a GPU backend for QOCO with CUDA kernels and a modular architecture, enabling large-scale problem solving with substantial speedups.

Findings

Achieved up to 70x speedup over CPU implementation.

Successfully handled large-scale problems with tens to hundreds of millions of nonzeros.

Provided a Python interface and CVXPY integration for ease of use.

Abstract

We present a GPU-accelerated backend for QOCO, a C-based solver for quadratic objective second-order cone programs (SOCPs) based on a primal-dual interior point method. Our backend uses NVIDIA's cuDSS library to perform a direct sparse LDL factorization of the KKT system at each iteration. We also develop custom CUDA kernels for cone operations and show that parallelizing these operations is essential for achieving peak performance. Additionally, we refactor QOCO to introduce a modular backend abstraction that decouples solver logic from the underlying linear algebra implementations, allowing the existing CPU and new GPU backend to share a unified codebase. This GPU backend is accessible through a direct Python interface and through CVXPY, allowing for easy use. Numerical experiments on a range of large-scale quadratic programs and SOCPs with tens to hundreds of millions of nonzero elements in the KKT matrix, demonstrate speedups of up to 50-70 times over the CPU implementation.