Advanced Computational Stochastic Dynamic Programming for Continuous Time Problems

首席研究员Hanson0207081和他的同事们开发了计算随机动态规划方法来寻找近似值，以最优地控制各种应用的期望目标值。这些应用包括化疗药物对癌症的最优治疗，最优金融投资组合和参数估计，随机制造系统的最优控制，以及地下水污染的最优修复。试验台的广泛应用有助于增加他们先进的数值方法的稳健性，因为它必须处理各种模型和边界条件。许多此类应用的另一个特征是，最严重的变化发生在系统的跳跃中，许多模型利用随机的跳跃扩散过程。在跳跃环境中计算最佳近似是模型的一个独特特征，其中模型的增加的真实感超过了由于扩散而增加的计算复杂性的额外负担。这位研究人员正在与一位同事一起撰写一本关于随机过程和控制的应用书籍，强调跳跃-扩散模型，以给它们更一般的结果带来更广泛的影响。数学水平是中级的，因此对于那些在科学、工程和金融领域实际应用的人来说，它是可以理解和有用的。主要研究人员和同事研究不确定环境中的系统模型，并寻求最优计算近似以获得这些系统的最佳性能。许多应用都是全国性的挑战。当癌细胞对癌症药物组合产生抗药性时，一种应用是癌症化疗的最佳管理。找到最佳癌症治疗计划的影响将是显著的，因为癌症是主要的死亡原因。另一种应用是对崩盘市场中最优投资者投资组合和消费问题的计算解决方案；其好处是更好地了解我们国家和世界的金融体系。第三个应用是制造系统在不确定故障、维修和其他中断情况下的最优调度。在这里，提高效率对国家经济福祉很重要。第四个应用是对周围水的污染进行最佳修复，这会产生重要的环境后果。学生参与了这些项目，为他们提供了在跨学科研究方面的重要经验。最后，研究人员正在撰写一本关于在具有大变化的不确定环境中的系统的最优控制的中级应用书籍，将他们的结果整合到广泛的应用中。其目的是将这些想法以一种更容易被科学家和工程师接受的形式带来。

Hanson0207081 The principal investigator and his colleagues developcomputational stochastic dynamic programming methods to findapproximations to optimally control the expected objective valuefor a wide variety of applications. These applications includethe optimal treatment of cancer by chemotherapy drugs, theoptimal financial investment portfolio and parameter estimation,optimal control of stochastic manufacturing systems, and theoptimal remediation of ground water pollution. The wide scope oftestbed applications helps to increase the robustness of theiradvanced numerical methods by having to treat a variety of modelsand boundary conditions. Another characteristic of many of theseapplications is that the most severe changes happen as jumps ofthe system and many models utilize stochastic jump-diffusionprocesses. The computation of optimal approximations in jumpenvironments is a unique feature of the models, where increasedrealism of the models more than compensates for the added burdenof increased computational complexity over diffusions. Theinvestigator is writing an applied book with a colleague onstochastic processes and control emphasizing jump-diffusionmodels to give broader impact to their more general results. Themathematical level is intermediate so that it is accessible anduseful to those who actually work with real applications inscience, engineering, and finance. The principal investigator and colleagues study models ofsystems in uncertain environments and seek optimal computationalapproximations to get the best performance from these systems.Many of the applications are national challenges. Oneapplication is the optimal management of cancer chemotherapy whencancer cells develop resistance to a cancer drug combination.The impact of finding optimal cancer treatment schedules would besignificant because cancer is a leading cause of death. Anotherapplication is computational solutions for optimal investorportfolio and consumption problems in a market with crashes invalue; the benefit is a better understanding of our nation's andthe world's financial systems. A third application is theoptimal scheduling of manufacturing systems subject to uncertainfailures, repairs, and other disruptions. Here improvedefficiencies are important for the national economic well-being.A fourth application is the optimal remediation of pollution inground water, with important environmental consequences. Studentsare involved in these projects, providing them with significantexperience in interdisciplinary research. Finally, theinvestigators are writing an intermediate level applied book onthe optimal control of systems in uncertain environments withlarge changes, integrating their results over a wide variety ofapplications. The aim is to bring these ideas in a moreaccessible form to scientists and engineers.