Analysis on polytopal structure of mathematical programs

数学规划就是在一定的约束条件下对给定的目标函数进行优化。已经有了各种快速求解数学规划的算法。虽然内点法在多项式时间内求解，但旋转算法仍有希望简化算法。在这项研究中，我们通过分析数学程序的多面体结构来研究旋转图的方向性质，以期提出更有效的旋转算法。

A mathematical program is to optimize a given objective function under some constraints. There have been various kinds of algorithms to solve mathematical programs rapidly. While the interior-point method solves them in polynomial time, pivoting algorithms are still promising for simplicity of the algorithms. In this research, we have studied properties of orientation of pivoting graphs by analyzing polytopal structure of mathematical programs, in order to propose more effective pivoting algorithms.