Nonlinear optimisation theory and algorithms provide a major mathematical foundation for many applications in data science and engineering. CAS and PolyU are working together to enhance mathematical foundations of nonlinear optimisation, which many tasks like predicting, forecasting, learning, reconstructing and controlling problems rely on. Despite advances in machine learning and AI, understanding the optimality, stability, and robustness of these models remains challenging. This collaboration looks to address three critical problems: 1) developing new mathematical optimisation theories; 2) creating efficient algorithms for min-max problems in GANs with non-smooth activation functions; 3) design problem-specific networks for rapid disaster response in smart cities. By addressing these theoretical gaps, the research may enhance the stability, robustness, and performance of optimisation models, advancing the field of data analytics and significantly contributing to applied mathematics, statistics, and machine learning.