论文标题
全局优化的顺序下降方法
A Sequential Descent Method for Global Optimization
论文作者
论文摘要
在本文中，提出了一种用于查找目标函数的全局最小值的顺序搜索方法，重复下降梯度搜索直到获得全局最小值为止。全球最低限度是通过寻找逐渐更好的本地最小值的过程。我们确定函数曲线与水平平面之间的相交点集，其中包含先前发现的局部最小值。然后，选择了最大的下降坡度的一个点，作为新的下降梯度搜索的初始点。该方法具有下降特性，并且收敛是单调的。为了证明所提出的顺序下降方法的有效性，解决了几个非凸多维优化问题。数值示例表明，可以通过提出的顺序下降方法寻求全局最小值。
In this paper, a sequential search method for finding the global minimum of an objective function is presented, The descent gradient search is repeated until the global minimum is obtained. The global minimum is located by a process of finding progressively better local minima. We determine the set of points of intersection between the curve of the function and the horizontal plane which contains the local minima previously found. Then, a point in this set with the greatest descent slope is chosen to be a initial point for a new descent gradient search. The method has the descent property and the convergence is monotonic. To demonstrate the effectiveness of the proposed sequential descent method, several non-convex multidimensional optimization problems are solved. Numerical examples show that the global minimum can be sought by the proposed method of sequential descent.
