9302926 Polak This is a three year proposal for research on the construction of efficient numerical methods, based on the concept of consistent approximations, for the solution of optimization problems arising in control, shape design, and integrated design of actively controlled structures. In particular, we will address the following issues: (i) the development of a general theory of algorithms based on consistent approximations for semi-infinite optimization, optimal control, and optimal shape design; (ii) the determination of the effects of the order and complexity of numerical integration formulae for ODE's and evolution on the computational efficiency of algorithms for the solution of optimal control problems, with control and state space constraints; (iii) the development of basic elements needed for the solution of shape optimization problems via consistent approximations, such as consistent optimality functions for shape optimization problems and their discrete approximations, numerical integration methods for PDE's that satisfy certain uniformity conditions, as well as subalgorithms that can cope efficiently with the very high dimensional problems that result from discretization. ***
