具有简单约束非线性规划的Hermite插值法

讨论具有简单约束非线性规划的求解方法 ,通过构造特殊结构的 Hermite插值公式 ,利用有效集的技巧 ,给出了求解这类问题的 Hermite插值算法。在通常的假设条件下 ,证明了算法具有全局收敛性。在严格互补松驰条件下 ,证明了算法在有限次迭代后有效约束集保持不变 ,从而使算法简化为求解无约束最优化的算法 ,有关收敛速度的结论相应成立

Hermite Interpolantion Algorithm for Nonlinear Programming with Simple Constraints

In this paper,we discuss nonlinear programming with simple constraints Using actively constrained set and special Hermite interpolantion,we give Hermite interpolantion algorithm for nonlinear programming with simple constraints Under milder conditions,we prove the global convergence of the algorithm It is alse proved that the correct active set can be identified in a finite number of iteration if strict complmentary slackness condition holds,and so the proposed algorithm reduces finally to an unconstrained minimization method in a limite number of iterations,allowing a fast asymptotic rate of convergence