SEMINAR

GlobSol and Global Search Algorithms for Global Optimization and Nonlinear Systems

Department of Mathematics
University of Lousiana at Lafayette

ABSTRACT

Most of the time researchers solve practical problems with software for nonlinear systems or nonlinear optimization, the software is based on local iterative methods. In such methods, an initial guess is given, and heuristic rules define an iteration scheme to refine the initial guess or move it towards the solution of the system. Often successful, even on certain large problems, these methods come with no guarantee to converge to a point near a solution, and they cannot find all solutions, if such solutions are not unique. Furthermore, even if such an iteration terminates successfully with an approximate solution, there is no guarantee that there is an actual solution within the user-specified tolerances of the given answer.

In the talk, we will introduce the concept of a verified method, in which the problem domain is exhaustively searched for all solutions. Although sometimes requiring a large computational effort and sometimes restricted to small numbers of variables, rigorous search techniques will give all solutions with mathematically rigorous bounds. Furthermore, due to quadratically convergent subprocesses, the techniques can often find all solutions surprisingly efficiently. We will illustrate this with our implementation, the GlobSol software package.

WHERE: TEC 205

WHEN(day): Friday, February 16th, 2001

WHEN(time): 2:00pm

EVERYBODY IS INVITED