A hybrid global optimization method: the one-dimensional case

We propose a hybrid global optimization method for nonlinear inverse problems. The method consists of two components: local optimizers and feasible point finders. Local optimizers have been well developed in the literature and can reliably attain the local optimal solution. The feasible point finder proposed here is equivalent to finding the zero points of a one-dimensional function. It warrants that local optimizers either obtain a better solution in the next iteration or produce a global optimal solution. The algorithm by assembling these two components has been proved to converge globally and is able to find all the global optimal solutions. The method has been demonstrated to perform excellently with an example having more than 1 750 000 local minima over [−106,107].