In this paper we consider the problem for finding the global minimum value of a continuous function over $R^n$. We show that, under a growth condition, the objective function which is non-smooth in general has a global minimizer on a closed ball. We pose a nonlinear diffusion equation concerning the optimization problem. A quasi-extremal flow is defined and constructed by the diffusion equation for an approximation to the minimum value of the global optimization problem. Several examples are presented to illustrate this computational approach.

中文翻译：

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扩散方程的非光滑优化计算方法

在本文中，我们考虑了寻找连续函数的全局最小值的问题。 ${\mathrm{[R}}^{ñ}$。我们表明，在增长条件下，通常不光滑的目标函数在闭合球上具有全局极小值。我们提出了关于优化问题的非线性扩散方程。通过扩散方程定义和构造准极值流，以近似于全局优化问题的最小值。给出了几个例子来说明这种计算方法。