School of Mathematical Sciences, Shenzhen University

Liyuan Distinguished Scholar Lecture Series Session 38

Lecture Title: Distributed Recursion Revisited

Speaker: Academician Yuhong Dai (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

Time: 2:30 PM - 3:30 PM, November 28, 2025

Venue: Classroom 2, Huixing Building, Yuehai Campus, Shenzhen University

Abstract: The distributed recursion (DR) algorithm is an effective method for solving the pooling problem that arises in many applications. It is based on the well-known P-formulation of the pooling problem, which involves the flow and quality variables; and it can be seen as a variant of the successive linear programming (SLP) algorithm, where the linear programming (LP) approximation problem can be transformed from the LP approximation problem derived by using the first-order Taylor series expansion technique. In this talk, we first propose a new nonlinear programming (NLP) formulation for the pooling problem involving only the flow variables, and show that the DR algorithm can be seen as a direct application of the SLP algorithm to the newly proposed formulation. With this new useful theoretical insight, we then develop a new variant of DR algorithm, called penalty DR (PDR) algorithm, based on the proposed formulation. The proposed PDR algorithm is a penalty algorithm where violations of the (linearized) nonlinear constraints are penalized in the objective function of the LP approximation problem with the penalty terms increasing when the constraint violations tend to be large. Compared with the LP approximation problem in the classic DR algorithm, the LP approximation problem in the proposed PDR algorithm can return a solution with a better objective value, which makes it more suitable for finding high-quality solutions for the pooling problem. Numerical experiments on benchmark and randomly constructed instances show that the proposed PDR algorithm is more effective than the classic SLP and DR algorithms in terms of finding a better solution for the pooling problem.

Speaker Profile: Yuhong Dai, optimization expert, Academician of the Chinese Academy of Sciences, Vice President, Researcher, and Doctoral Supervisor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He currently serves as President of the Chinese Operations Research Society, Vice President of the Chinese Mathematical Society, and Vice President of the International Federation of Operational Research Societies (IFORS).

Academician Yuhong Dai has long dedicated himself to research in optimization and artificial intelligence, achieving systematic and creative results in nonlinear optimization, integer programming, and applied optimization. His work has garnered extensive citations and acclaim from both theoretical and applied communities. The Dai-Yuan method, co-proposed by him, is recognized internationally as one of the four most significant nonlinear conjugate gradient methods. He independently resolved the open convergence problem of the internationally renowned BFGS quasi-Newton method. While establishing the superlinear convergence theory for gradient methods, he also proposed the Dai-Fletcher method. Addressing core optimization challenges in aerospace, communications, energy, and logistics, he and his collaborators developed a series of efficient algorithms and independently created China's first modern mixed-integer programming solver, CMIP. Starting from spacecraft online trajectory optimization and wireless communication joint access and power control problems, he and his team proposed the theory and fundamental algorithms for minimum constraint violation optimization, overcoming the limitations of classical KKT stable points by introducing D-stable points.

Academician Yuhong Dai has received the Second Prize of the National Natural Science Award (2006, second author), the Feng Kang Prize for Scientific Computing (2015), the Shiing Shen Chern Mathematics Award in Mathematics from the Chinese Mathematical Society (2017), the inaugural Xiao Shu-Tie Applied Mathematics Prize from the China Society for Industrial and Applied Mathematics (2018), and the Operations Research Application Award from the Chinese Operations Research Society (2018). She delivered a 45-minute invited talk at the 2022 International Congress of Mathematicians and a one-hour plenary lecture at the 2022 International Congress on Operations Research. She leads the National Natural Science Foundation of China's Innovative Research Group Project and the Ministry of Science and Technology's Key R&D Program. Elected Fellow of the Chinese Society for Industrial and Applied Mathematics in 2021, Fellow of the Chinese Operations Research Society in 2022, and Fellow of the International Federation of Operational Research Societies in 2023. Elected Academician of the Chinese Academy of Sciences in 2025.

All faculty and students are welcome to attend!

School of Mathematical Sciences

November 27, 2025