解非线性约束方程的拉格朗日全局投影方法

基于最优化方法求解约束非线性方程组的一个突出困难是计算 得到的仅是该优化问题的稳定点或局部极小点,而非方程组的解点.由此引出的问题是如何从一个稳定点出发得到一个相对于方程组解更好的点. 该文采用投影型算法,推广了Nazareth-Qi$^{8,9]}$ 求解无约束非线性方程组的拉格朗日全局算法(Lagrangian Global-LG)于约束方程上; 理论上证明了从优化问题的稳定点出发,投影LG方法可寻找到一个更好的点. 数值试验证明了LG方法的有效性.

Lagrangian Globalization Projection Methods for Nonlinear Constrained Equations

To solve constrained nonlinear equations based on optimizationalgorithms is suffered a difficulty that the authors obtain just a stationary point or a local minimizer of the underlying optimization problem, which is not necessarily a solution of the equations. Then the arising problem is how to get a better point from the stationary point or the local minimizer point. By using a projection-type method, this paper extends the Lagrangian globalization (LG) method 8, 9] to a system ofnonlinear equations with bounded constraints. The authors prove that from a stationary point, the LG projection method can find a better point. Numerical examples also show that the LG method has a potential to escape the stationary point of optimization problems.