A New Approach to Global Optimiation by an Adapted Diffusion
In this paper, we study a problem of global optimization of an energy functional by a stochastic dynamics with a general diffusion coefficient. The main result is that adapting the diffusion coefficient to the shape of the functional enables the dynamics to escape wide local minima, and attracts it to narrower global minima that are missed by conventional diffusions. We discuss how to properly choose the diffusion coefficient and show numerically the superior performance of the resulting optimization algorithm.