Algorithm 1055: HDSDP: Software for Semidefinite Programming

HDSDP is a numerical software solving semidefinite programming problems. The main framework of HDSDP resembles the dual-scaling interior point solver DSDP and several new features, including a dual method based on the simplified homogeneous self-dual embedding, have been implemented. The embedding technique enhances the stability of the dual method, and several new heuristics and computational techniques are designed to accelerate its convergence. HDSDP aims to show how the dual-scaling algorithm benefits from the self-dual embedding, and it is developed in parallel to DSDP 5.8. Numerical experiments over several classical benchmark datasets exhibit their robustness and efficiency, particularly their advantages on SDP instances featuring low-rank structure and sparsity. HDSDP is open sourced under an MIT license and available at https://github.com/Gwzwpxz/HDSDP .