A model problem for global optimization

Abstract

: We present a model problem for global optimization in a specified number of unknowns. We give constraint and unconstraint formulations. The problem arose from structured condition numbers for linear systems of equations with Toeplitz matrix. We present a simple algorithm using additional information on the problem to find local minimizers which presumably are global. Without this it seems quite hard to find the global minimum numerically. For dimensions up to n = 18 rigorous lower bounds for the problem are presented.