Cross-Hill: A heuristic method for global optimization

The heuristic Cross-Hill method proposed by Qi et al. (2009) [14] was recently extended from finding the Z-eigenvalues of tensors to quantum separation problem by Han and Qi (2013) [5]. In this paper, we show that it can be extended to solve general global optimization problems. The heuristic Cross-Hill method is a combination of a local optimization method and a global optimization method with lower dimension. At each iteration, it first uses the local optimization method to find a local solution. Then, using this point and an arbitrary orthogonal vector, it solves a two-dimensional optimization problem to find a better solution than that the local approach was able to find. Preliminary experimental results are very encouraging.