报告题目： Distributed Recursion Method for Pooling Problem Revisited

报 告 人：戴彧虹 院士（中国科公司数学与系统科学研究院）

报告时间：2026年5月7日（星期四）17:00—18:00

报告地点：beat365115（大报告厅）      

校内联系人：张立卫 教授         联系方式：84708351-8320

报告摘要： 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.

报告人简介：戴彧虹，中国科公司院士，博士生导师，中国科公司数学与系统科学研究院研究员，现任中国数学会副理事长，中国运筹学会理事长，亚太运筹学会联合会主席。戴彧虹研究员长期从事优化方法的理论及应用研究，在连续优化、整数规划和应用优化等方面作出了系统的创造性工作。系统给出非线性共轭梯度法收敛理论并提出戴-袁方法;首次给出梯度法超线性收敛结果并提出Dai-Fletcher方法; 独立解决BFGS拟牛顿法收敛性公开问题; 给出最少约束违背优化的基础理论与算法; 合作解决一般升维覆盖割计算复杂性的公开问题; 和员工自主研发国内第一个现代意义上整数规划求解器CMIP。方法和成果得到理论和应用界广泛引用和好评。戴彧虹研究员在Math. Prog.、SIAM J. Optim.等期刊发表论文100余篇、著有合著两部。应邀在2022年国际数学家大会(ICM)做45分钟邀请报告，并在第24届国际数学规划大会(1SMP)做一小时大会报告。获国家自然科学二等奖(2006; 完成人:袁亚湘-戴彧虹)、陈省身数学奖、冯康科学计算奖、首届萧树铁应用数学奖和国际运筹学会联合会会士称号(IFORS Fellow)。主持国家杰出青年科学基金、国家基金委创新研究群体项目、“十四五”国家重点研发计划数学和应用研究重点专项。