Multistage Stochastic Convex Optimization

点击翻译按钮获取中文摘要

Optimization problems with uncertainty are encountered in many applications. Some examples that have received a fair amount of attention include inventory control with uncertain demand, investment portfolio selection with uncertain returns and liabilities, and electricity generation with uncertain demand. There are various approaches to modeling and solving such problems. The investigators consider Multistage Stochastic Programming and Dynamic Programming problems in which a sequence of decisions is made and some of the problem parameters are random, and information that can be used in later decisions become available over time. Considerable progress has been made in the last few years in our ability to handle optimization problems with uncertainty. It was shown theoretically and confirmed in numerical experiments that sampling methods allow solving some of these problems with proven accuracy and in some cases even exactly. It seems that we now have a sound theoretical background and some numerical experience indicating that come types of problems can be solved effectively by sampling techniques. The proposed research is aimed at developing basic theory and numerical procedures for solving multistage optimization problems with uncertainty. In order to make them work, effective deterministic optimization algorithms should be combined with simulation methods in an efficient way. If successful, it may open the possibility to solve a considerably larger class of real world problems. In that respect theoretical results and preliminary numerical experiments with the suggested approach are quite encouraging.