Stochastic Differential Equation of the Quantization based Optimization.

We propose a stochastic differential equation for a quantization-based optimization algorithm. A fundamental differential equation describes the state transition by an algorithm to analyze the dynamics of an optimization algorithm. According to the White Noise Hypothesis of quantization error with dense and uniform distribution, we can regard the quantization error as an identically independent distribution(i.i.d.) white noise. It leads that we can obtain a stochastic equation about the quantization-based optimization algorithm to analyze the global dynamics. Numerical experiments show that the proposed algorithm involves better performance than the conventional optimization algorithm, such as simulated annealing.