基于动力系统求非线性优化的局部最优解

摘要

According to the topological and geometric properties of the objective function the multiple local optimal solutions were solved, and relevant gradient vector field of the function was established.The stable equilibrium of the gradient vector field was the local optimal so-lution of the corresponding objective function.Through degradation point of gradient vector field seeks for the stable equilibrium.This paper improved the method of degradation point algorithm and solve nonlinear optimization of multiple locally optimal solutions.%根据目标函数的拓扑和几何性质求函数的多个局部最优解,建立相关的梯度向量场,求梯度向量场的稳定均衡点,稳定均衡点就是相应目标函数的局部最优解,通过退化点使梯度向量场跳出稳定均衡点的稳定域,在本文中对求退化点的算法进行改进,求非线性优化的多个局部最优解.