In this paper we show that the unconstrained continuous global minimization problem can not be solved by any algorithm. So without loss of generality we consider the box constrained continuous global minimization problem. We present a new globally convexized filled function method for the problem. The definition of globally convexized filled function is adapted from that by Ge and Qin [7] for unconstrained continuous global minimization problems to the box constrained case. A new class of globally convexized filled functions are constructed. These functions contain only one easily determinable parameter. A randomized algorithm is designed to solve the box constrained continuous global minimization problem basing on these globally convexized filled functions. The asymptotic convergence of the algorithm is established. Preliminary numerical experiments show that the algorithm is practicable.
Citation
Department of Computer Science and Technology, Fuzhou University, Fuzhou 350002, China, 03/2004.