Abstract: The problems of nonlinear equations are a class of classical numerical calculation problems, and the simple evolutionary algorithm requires not only a high degree of evolution algebra, but also can not 100% guarantee to converge to the global optimal solution. To solve this problem, Particle Swarm Optimization and Proximal Point Algorithm are mixed, and the Proximal Point Algorithm is used as the outer layer algorithm, and the Particle Swarm Optimization is used as the inner layer algorithm to solve the problems of nonlinear equations. The algorithm has better effects of computation for convex problems, which is an effective algorithm of solving nonlinear equations.

Key words: Particle Swarm Optimization（PSO）, Proximal Point Algorithm（PPA）, systems of nonlinear equations

摘要： 非线性方程组问题是一类经典的数值计算问题，单纯的进化算法不但需要很高的进化代数，而且也不能保证100%收敛到全局最优解。为求解此问题，把粒子群算法和邻近点算法相混合，利用邻近点算法作为外层算法，粒子群算法作为内层算法进行求解。实验结果表明该算法对凸问题有较好的计算效果，是求解非线性方程组问题的一种有效算法。

关键词: 粒子群算法, 邻近点算法, 非线性方程组问题