AF: EAGER: Algorithms in Linear Algebra and Optimization

舒尔曼博士的研究将解决计算机科学中的两个核心问题：(1)强多项式时间内的线性规划和(2)对角线平衡的矩阵预条件。强多项式时间线性规划算法将是复杂性理论在实数域上的一次突破。它可能导致改进的算法，用于更难的类型的凸规划(例如，半定的)，这些规划(尽管是在多项式时间内)目前是非常慢的。更好的矩阵预条件算法有可能显著改进线性代数软件包。

Dr. Schulman's research will tackle two problems of central importance in computer science: (1) Linear programming in strongly polynomial time and (2) Matrix pre-conditioning by diagonal balancing. A strongly polynomial-time algorithm for linear programming would be a breakthrough in complexity theory over the real field. It may lead to improved algorithms for harder types ofconvex programming (e.g., semidefinite) which (albeit in polynomial time) are currently prohibitively slow. Better algorithms for matrix preconditioning have the potentially to significantly improve linear algebra software packages.