Global Optimization with a Power-Transformed Objective and Gaussian Smoothing

We propose a novel method that solves global optimization problems in two steps: (1) perform a (exponential) power-N transformation to the not-necessarily differentiable objective function f and get f N , and (2) optimize the Gaussian-smoothed f N with stochastic approximations. Under mild conditions on f , for any δ > 0, we prove that with a sufficiently large power N δ , this method converges to a solution in the δ-neighborhood of f 's global optimum point. The convergence rate is O(d 2 σ 4 ε -2 ), which is faster than both the standard and single-loop homotopy methods if σ is preselected to be in (0, 1). In most of the experiments performed, our method produces better solutions than other algorithms that also apply smoothing techniques.