求解非线性等式和不等式问题的一种光滑化算法

A smoothing method for solving the nonlinear system of equalities and inequalities

给出了求解非线性等式和不等式问题的一种新算法.用Max函数将不等式约束转变为等式约束,建立了一个半光滑的无约束方程组系统,并设计了一种光滑化Gauss-Newton算法求解该系统.在适当条件下,证明了此算法的全局和局部收敛性.数值实验表明此方法的有效性.

It is concerned with a new algorithm for solving the nonlinear system of equalities and inequalities. By using the so - called max function, the inequalities are transfered into equalities and a system of semismooth equations is set. Then a smoothing Gauss - Newton method is introduced for solving the reformulated system. The global and local convergence are studied under suitable conditions. Numerical examples are given to show that the new approach is effective.