Professor Han proposes to study new theoretical and computational aspects of certain optimization problems. His main interests lie in designing a conceptual framework for computer oriented procedures that seek a minimum of a function of many variables subject to constraints. The class of problems that Han is studying involves smooth, i.e. differentiable functions of n variables which may be approximated by quadratic functions. The variables are not restricted to integer values. This class of problems is often solved by iterative methods in which the minimization is done sequentially by searching for minimum of the function along certain special directions. With the development of new computer architectures it became more and more important to adapt the existing procedures to new possibilities. In parallel processing, arithmetic and logical operations can be done by many processors at the same time. Han proposes to investigate minimization methods that are based on a decompositon of the problem into several search problems with directions that are independent in a certain sense. Such techniques could become useful in parallel processing and could yield a important speed-up of practical computing.
