Advanced Computational Stochastic Dynamic Programming for Continuous Time Problems

首席研究员和他的同事们开发了计算随机动态规划方法，以找到最优控制各种应用的预期目标值的近似值。这些应用包括化疗药物对癌症的最佳治疗，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提高其先进的数值方法的鲁棒性，因为必须处理各种模型和边界条件。许多这些应用的另一个特点是，最严重的变化发生在系统的跳跃和许多模型利用随机跳跃扩散过程。跳跃环境中最优近似的计算是模型的一个独特特征，其中模型的真实感增加了对扩散计算复杂性增加的额外负担的补偿。研究人员正在与同事撰写一本关于随机过程和控制的应用书籍，强调跳跃扩散模型对其更一般的结果产生更广泛的影响。数学水平是中等的，所以对于那些在科学、工程和金融领域实际应用的人来说，它是容易理解和有用的。首席研究员及其同事研究不确定环境中的系统模型，并寻求最佳计算近似，以获得这些系统的最佳性能。许多申请都是全国性的挑战。一个应用是癌症化疗的最佳管理，当癌细胞对癌症药物组合产生耐药性时。找到最佳的癌症治疗方案的影响将是重大的，因为癌症是导致死亡的主要原因。另一个应用是价值崩溃市场中最优投资者投资组合和消费问题的计算解决方案；这样做的好处是更好地了解我们国家和世界的金融体系。第三个应用是针对不确定故障、维修和其他中断的制造系统的最佳调度。在这方面，改善不足对国民经济福祉至关重要。第四个应用是对具有重要环境后果的地下水污染的最佳补救。学生参与这些项目，为他们提供跨学科研究的重要经验。最后，研究人员正在撰写一本关于大变化不确定环境中系统最优控制的中级应用书籍，将他们的结果整合到各种应用中。其目的是让科学家和工程师更容易理解这些想法。

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.