HDSDP: Software for Semidefinite Programming

TL;DR

HDSDP is an open-source software that improves semidefinite programming solutions by integrating a dual-scaling method with self-dual embedding, demonstrating robustness and efficiency especially on low-rank and sparse problems.

Contribution

The paper introduces HDSDP, a new semidefinite programming solver that incorporates a simplified homogeneous self-dual embedding into a dual-scaling framework, enhancing stability and convergence.

Findings

Shows robustness on classical benchmarks

Efficient on low-rank and sparse SDP instances

Developed in parallel with DSDP5.8

Abstract

HDSDP is a numerical software solving the semidefinite programming problems. The main framework of HDSDP resembles the dual-scaling interior point solver DSDP [BY2008] and several new features, including a dual method based on the simplified homogeneous self-dual embedding, have been implemented. The embedding technique enhances stability of the dual method and several new heuristics and computational techniques are designed to accelerate its convergence. HDSDP aims to show how dual-scaling algorithm benefits from the self-dual embedding and it is developed in parallel to DSDP5.8. Numerical experiments over several classical benchmark datasets exhibit its robustness and efficiency, and particularly its advantages on SDP instances featuring low-rank structure and sparsity. HDSDP is open-sourced under MIT license and available at https://github.com/COPT-Public/HDSDP.