关于非线性不等式组Levenberg-Marquardt算法的收敛性(英文)

ON THE CONVERGENCE OF LEVENBERG-MARQUARDT METHOD FOR NONLINEAR INEQUALITIES

本文研究了一类非线性不等式组的求解问题.利用一列目标函数两次可微的参数优化问题来逼近非线性不等式组的解,光滑Levenberg-Marquardt方法来求解参数优化问题,在一些较弱的条件下证明了文中算法的全局收敛性,数值实例显示文中算法效果较好.

In this article, we study the solutions for a class of nonlinear inequalities. The nonlinear inequalities are approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions, then a smoothing Levenberg-Marquardt method is applied to solve the parameterized optimization problems. The global convergence of the proposed method is established under some weak conditions. Numerical results show that the method performs well.