A Smoothing Method of Global Optimization that Preserves Global Minima

A new smoothing method of global optimization is proposed in the present paper, which prevents shifting of global minima. In this method, smoothed functions are solutions of a heat diffusion equation with external heat source. The source helps to control the diffusion such that a global minimum of the smoothed function is again a global minimum of the cost function. This property, and the existence and uniqueness of the solution are proved using results in theory of viscosity solutions. Moreover, we devise an iterative equation by which smoothed functions can be obtained analytically for a class of cost functions. The effectiveness and potential of our method are then demonstrated with some experimental results.

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