A sequential convexification method (SCM) for continuous global optimization

A new method for continuous global minimization problems, acronymed SCM, is introduced. This method gives a simple transformation to convert the original objective function to an auxiliary function with gradually fewer local minimizers. All Local minimizers except a prefixed one of the auxiliary function is in the region where the function value of the original objective function is lower than a current minimal value. We use BFGS local optimizer with an inexact line search method to minimize the auxiliary function to find a local minimizer at which the original objective function value is lower than the current minimal value. Numerical experiments on a set of standard test problems with several problems' dimensions up to 50 show that our algorithm is efficient comparing with other global optimization methods.


Technical Report, 06/2001 Department of Computer Science Fuzhou University Fuzhou 350002 P.R. China