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 fN, and (2) optimize the Gaussian-smoothed fN with stochastic approximations. Under mild conditions on f, for any δ>0, we prove that with a sufficiently large power Nδ, this method converges to a solution in the δ-neighborhood of f's global optimum point. The convergence rate is O(d2σ4varepsilon-2), which is faster than both the standard and single-loop homotopy methods if σ is pre-selected to be in (0,1). In most of the experiments performed, our method produces better solutions than other algorithms that also apply smoothing techniques.