报告题目：Basis partition of the space of linear programs through a differential equation

报告人：赵公允

报告时间：2024年1月13日9:00-11:30

报告地点：88038威尼斯302

邀请单位：88038威尼斯

报告内容简介：

Each linear program (LP) has an optimal basis. The space of linear programs can be partitioned according to these bases, so called the basis partition. Discovering the structures of this partition is our goal. We represent the space of linear programs as the space of projection matrices, i.e. the Grassmann manifold. A dynamical system on the Grassmann manifold is used to characterize the basis partition as follows: From each projection matrix associated with an LP, the dynamical system defines a path and the path leads to an equilibrium projection matrix which determines the optimal basis of the LP. All projection matrices which lead to an optimal basis form a set, and these sets partition the Grassmann manifold. Properties of the dynamical system, e.g. eigenvalues and eigenvectors, stable and unstable manifolds, etc, provide useful tools for constructing the partition.

报告人简介：

赵公允（GongyunZhao），新加坡国立大学教授。本科、硕士期间均就读于厦门大学，博士毕业于 University of Würzburg。研究方向为最优化理论与方法，其研究成果在数学优化领域顶级期刊 Mathematical Programming, SIAM Journal on Optimization, Mathematics of Operations Research 等发表多篇学术论文。曾担任第 15 届数学优化全球论坛咨询委员会委员，2003-2011 担任 SCI 期刊 Asia-Pacific Journal of Operational Research 主编。