mwang (04/26/83)
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF WATERLOO SEMINAR ACTIVITIES NUMERICAL ANALYSIS SEMINAR - Tuesday, May 3, 1983. Dr. G.T. Timmer of Erasmus Universiteit will speak on ``Stochastic Methods for Unconstrained and Constrained Global Optimization''. TIME: 3.30 PM ROOM: MC 5158 ABSTRACT Stochastic techniques enter the design as well as the analysis of several efficient methods to find the glo- bal minimum of a function f over a compact set S. A method will be presented where in each iteration a group of points randomly drawn from a (possibly chang- ing) distribution over S are added to a sample and a procedure similar to clustering is applied to a (possi- bly changing) fraction of this sample. This is done in such a way that the clusters found correspond to re- gions of attraction of f. Inside each newly found re- gion of attraction a local search is initiated. The method is (asymptotically) provably correct and prov- ably fast: the expected running time in iteration k does not depend on k , but is bound by a constant. Under various probabilistic assumptions about f and its local minima, the probability distribution of the actual number of local minima and the relative measure of their regions of attraction can be derived in a Bayesian manner. This can be used to formulate proper stopping criteria for the method described. All these ideas can be applied to both unconstrained and constrained global optimization. In the case of constrained global optimization, the restricted problem is transformed to an unrestricted one using a so-called doubly-exact penalty function. This penalty function has the property that there is a 1-1 correspondence between the local minima of the constrained and the un- constrained problem. April 26, 1983