一种求解非线性方程组的混沌优化算法

A Chaos Optimization Algorithm for Solving Nonlinear Equations

本文针对非线性方程组的求解问题提出一种混合算法,将方程组转换成一个优化问题。将优化问题的非线性共轭梯度法与混沌优化方法相结合,提出了一种新的混合优化算法。该算法能使非线性共轭梯度法跳出局部最优,最终获得全局最优。算法的收敛性也进行了证明,数值结果表明该算法是有效的。

In this paper, a hybrid algorithm for solving the nonlinear equations is proposed. The equations are transformed into an optimization problem. A new hybrid algorithm that combines the chaos optimization method and the nonlinear conjugate gradient method having an effective convergence property is introduced. The hybrid algorithm can help the conjugate gradient approach to skip the local minimum. Finally, it can find the global minimum. The convergence of the algorithm is thus proved. An example is provided to prove the efficiency of this algorithm.