Advanced Computational Stochastic Dynamic Programming for Continuous Time Problems

University Of Illinois At Chicago, Chicago IL

Investigators

Abstract

Hanson 0207081 The principal investigator and his colleagues develop computational stochastic dynamic programming methods to find approximations to optimally control the expected objective value for a wide variety of applications. These applications include the optimal treatment of cancer by chemotherapy drugs, the optimal financial investment portfolio and parameter estimation, optimal control of stochastic manufacturing systems, and the optimal remediation of ground water pollution. The wide scope of testbed applications helps to increase the robustness of their advanced numerical methods by having to treat a variety of models and boundary conditions. Another characteristic of many of these applications is that the most severe changes happen as jumps of the system and many models utilize stochastic jump-diffusion processes. The computation of optimal approximations in jump environments is a unique feature of the models, where increased realism of the models more than compensates for the added burden of increased computational complexity over diffusions. The investigator is writing an applied book with a colleague on stochastic processes and control emphasizing jump-diffusion models to give broader impact to their more general results. The mathematical level is intermediate so that it is accessible and useful to those who actually work with real applications in science, engineering, and finance. The principal investigator and colleagues study models of systems in uncertain environments and seek optimal computational approximations to get the best performance from these systems. Many of the applications are national challenges. One application is the optimal management of cancer chemotherapy when cancer cells develop resistance to a cancer drug combination. The impact of finding optimal cancer treatment schedules would be significant because cancer is a leading cause of death. Another application is computational solutions for optimal investor portfolio and consumption problems in a market with crashes in value; the benefit is a better understanding of our nation's and the world's financial systems. A third application is the optimal scheduling of manufacturing systems subject to uncertain failures, repairs, and other disruptions. Here improved efficiencies are important for the national economic well-being. A fourth application is the optimal remediation of pollution in ground water, with important environmental consequences. Students are involved in these projects, providing them with significant experience in interdisciplinary research. Finally, the investigators are writing an intermediate level applied book on the optimal control of systems in uncertain environments with large changes, integrating their results over a wide variety of applications. The aim is to bring these ideas in a more accessible form to scientists and engineers.