On September 28, a research team from the Antai College of Economics and Management (ACEM) and the Institute for Intelligent Computing (IIC) at Shanghai Jiao Tong University, together with collaborators, published a paper titled "Large-scale semidefinite programming with graphics processing units" in the Proceedings of the National Academy of Sciences (PNAS). By co-designing mathematical optimization algorithms with GPU architectures, the team has significantly improved the efficiency of solving large-scale semidefinite programming (SDP) problems, providing a high-performance computational foundation for AI for Science (AI4S).

The first author, Qiushi Han, received early research training under the team's guidance as an undergraduate and is now pursuing a PhD at the Massachusetts Institute of Technology (MIT). The second author, Zhenwei Lin, is a doctoral student under the supervision of Qi Deng. Qi Deng, Dongdong Ge and Yinyu Ye are all faculty members at SJTU's Institute for Intelligent Computing (IIC), with Prof. Dongdong Ge and Prof. Caihua Chen of Nanjing University serving as co-corresponding authors.

SDP is widely used in combinatorial optimization, machine learning, control and quantum science, yet traditional methods are often constrained by computation time and memory capacity. Rather than simply porting CPU code, the team's GPU-accelerated solver, cuLoRADS, redesigns the core computational pipeline by combining low-rank factorization, splitting algorithms and GPU parallelism — reducing memory requirements and pushing the boundaries of what can be solved at massive scale.

In experiments, cuLoRADS solved a set of max-cut SDP relaxations with 10-million-dimensional matrix variables in 10 seconds to 1 minute each on a single NVIDIA H100 GPU, compared with dozens of hours for previously reported CPU methods. Within minutes, the solver also handled a max-cut relaxation with a 170-million-dimensional matrix variable and a matrix completion problem with approximately 200 million constraints.

cuLoRADS has since been applied across several scientific frontiers. In quantum ordered search, the team collaborated with the quantum computing group at Peking University to break through the computational bottleneck of six-query scenarios and advance the complexity upper bound of quantum search; the work has been accepted at ICML 2026. In embodied intelligence, the team worked with Heng Yang's group at Harvard University to validate GPU-based optimization methods in robot trajectory planning and model predictive control, improving precise control under complex constraints. In quantum chemistry, the team has partnered with Google Quantum AI to use cuLoRADS in computing lower bounds on molecular ground-state energy, helping reduce the resource cost of quantum simulation; the results were published in Physical Review X (PRX).

From fundamental methods in management science to quantum science and embodied intelligence, the work highlights Antai's strength in cross-disciplinary innovation and its success in engaging undergraduates in research from an early stage. The team will continue to integrate optimization theory, algorithms and heterogeneous computing, providing foundational support for AI4S and intelligent decision-making.