This project will study the design and analysis of algorithms for the solution of large scale optimization problems and nonlinear equations that arise from discretizations of infinite dimensional problems. The goals include development of a unifying theory for pointwise quasi-Newton methods, study of the symmetric rank one method in infinite dimensions in both the conventional and pointwise contexts, analysis of a new class of methods that use the step in finite difference computation of gradients as a tool to avoid local minima for problems that are sums of simple smooth functions and small amplitude, high frequency, noise terms, and globally convergent algorithms for infinite dimensional problems. The basic research will be applied to problems in radiative transfer, computer sided design of microwave devices, and numerical methods for optimization of competitive systems.
