Abstract

The problem of finding the global minimum of a nonnegative function on a positive parallelepiped in n-dimensional Euclidean space is considered. A method for localizing false extrema in a bounded domain near the origin is proposed, which allows one to separate the global minimum from the false ones by moving the former away from the latter. With a suitable choice of the starting point in the gradient descent method, it is possible to prove the convergence of the iterative sequence to the global minimum of the function.

中文翻译：

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全局优化中的假极值定位方法

摘要

考虑在n维欧几里德空间中寻找正平行六面体上非负函数的全局最小值的问题。提出了一种在原点附近的有界域中定位虚假极值的方法，该方法允许通过将前者远离后者来将全局最小值与虚假极值分开。通过在梯度下降法中适当选择起点，可以证明迭代序列收敛到函数的全局最小值。