ABSTRACT

As a complement to two recent papers by Toan and Yao (Mordukhovich subgradients of the value function to a parametric discrete optimal control problem. J Global Optim. 2014;58:595–612), and by An and Toan (Differential stability of convex discrete optimal control problems. Acta Math Vietnam. 2018;43:201–217) on subdifferentials of the optimal value function of discrete optimal control problems, this paper studies the differential stability of convex discrete optimal control problems under control constraints, where the solution set may be empty. By using a suitable sum rule for ϵ-subdifferentials and a suitable product rule for ϵ-normal directions, we obtain formulas for computing the ϵ-subdifferential of the optimal value function. Several illustrative examples are also given.

摘要

作为对 Toan 和 Yao 最近两篇论文的补充（Mordukhovich subgradients of the value function to a parametric Discrete optimization control problem. J Global Optim. 2014;58:595–612），以及 An 和 Toan（凸离散的微分稳定性）最优控制问题. Acta Math Vietnam. 2018;43:201-217) 关于离散最优控制问题的最优值函数的次微分，本文研究了控制约束下凸离散最优控制问题的微分稳定性，其中解集可能为空。通过对ϵ -subdifferentials使用合适的求和规则和对ϵ -normal方向使用合适的乘积规则，我们获得了计算ϵ的公式-最优价值函数的次微分。还给出了几个说明性示例。