多维参数线性规划的解分割和方向导数

Partition of solutions and directional derivatives for linear programming problem with higher-dimensional parameters

基于最优分割的概念,消费系数多维参数化的线性规划的最优值函数和临界域特征被研究.证明了最优值函数的有效域可分解为有限多个相对内部不交的临界域,这是不同于基于最优基概念所得结论.并给出一个求解任何点处任何方向导数的线性规划方法.

Based on the concept of the optimal partition, the characters of the optimal value function and the critical regions for linear programming problem with higher-dimensional parametric cost coefficients are studied. It is shown that the domain of the optimal value function can be decomposed into finitely many critical regions with disjoint relative interiors, which is different from the result based on the concept of the optimal basis. A linear programming method by which any directional derivative at any point can be computed is given.