论文标题
参数圆锥线性编程中的两个最佳值函数
Two Optimal Value Functions in Parametric Conic Linear Programming
论文作者
论文摘要
我们考虑由欧几里得空间和矩阵中的封闭凸锥给出的圆锥线性程序，其中约束系统的右侧向量和定义目标函数的向量会发生变化。使用严格的可行性条件，我们证明了局部Lipschitz的连续性，并在右侧扰动下获得了问题的最佳值函数的一些不同性能。对于目标函数的线性扰动下的最佳价值函数，在假设下获得了类似的可区分性能，即原始问题和双重问题都是严格可行的。
We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand-side of the constraint system and the vector defining the objective function are subject to change. Using the strict feasibility condition, we prove the locally Lipschitz continuity and obtain some differentiability properties of the optimal value function of the problem under right-hand-side perturbations. For the optimal value function under linear perturbations of the objective function, similar differentiability properties are obtained under the assumption saying that both primal problem and dual problem are strictly feasible.
