9500957 Rockafeller This project centers on optimization problems concerned with the management or control of systems with dynamical structure. For problems in continuous time, such as arise in the optimal control mf engineering systems and economic models, new forms of variational analysis will be developed in order to characterize solutions more concretely and in a wider variety of settings. In particular, issues of solution stability will be studied. For problems in discrete time, models of decision-making under uncertainty will be the focus. Connections between stochastic programming and dynamic programming will be elucidated and made the basis of new approaches to the design of computational methods for finding solutions. The work will deal with mathematical innovations necessary to understand the effects of different control strategies in situations that heretofore have resisted effective modeling. Especially important are the ways of representing mathematically the revelation over time of information about random elements in a problem's structure. A combination of scenario trees with state-variable dynamics will be explored for this purpose. Extended linear-quadratic programming will be utilized to allow penalty expression of constraints and to promote dualization leading to numerical schemes in which problems of enormous scale can be broken down iteratively into problems solvable on high-speed computers. ***
