论文标题
COVID-19锁定的简单计划问题：一种动态的编程方法
A simple planning problem for COVID-19 lockdown: a dynamic programming approach
论文作者
论文摘要
许多最近的研究都考虑了一个隔间SIR模型，用于研究旨在包含Covid-19的最佳控制政策，同时最大程度地减少预防措施的经济成本。此类问题是非凸，标准结果不必保持。我们使用动态编程方法，并证明了相关优化问题的价值函数的某些连续性属性。我们研究了相应的汉密尔顿 - 雅各比 - 贝尔曼方程，并表明该值函数在粘度意义上解决了它。最后，我们讨论一些最佳条件。我们的论文代表了在动态编程方法中对非凸动动态优化问题进行完整分析的首次贡献。
A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach.
