非线性规划的一个罚内点方法

A Penalty Interior-Point Method for Nonlinear Programming

针对具有不等式约束的非线性规划,结合罚内点途径,且在牛顿法的基础上,提出一个算法.通过引入辅助变量松弛不等式约束,把约束集合转化为两个集合的交集:一个是容易计算内点的,另一个是简单线性的.这样就提出了解决此问题的一个新的障碍和罚函数方法且给出了其方法的一般收敛性结果.对接近度量和算法参数的选择途径也进行了研究,从而程序上保证了一旦障碍参数被更新,算法仅需要有限牛顿步就能达到近似中心.数值例子说明了方法的有效性.

The paper presents an algorithm, combining the penalty and interior-point approaches for nonlinear programming with inequality constraints, based on Newton＇s method. By using an auxiliary variable to relax the inequality constraints, the constraint set is turned into an intersection of two sets： one of them has an easy computable interior, and the other one is simply affine linear. Then, a new combined barrier and penalty function approach is proposed to solve this problem. A general convergence result of our method is shown. The proximity measure and the algorithmic parameter selection issues are studied. The procedure thus ensures that it require only a finite number of Newton steps to reach an approximate center once the barrier/penalty parameter is updated. Numerical examples are presented to show the effectiveness of the method.