有界变量约束优化的仿射尺度不精确牛顿法

采用内点线搜索技术，提出了一种新的仿射尺度不精确牛顿方法求解有界变量约束的非线性优化问题．选取光滑的尺度矩阵，并通过变换为有界约束的最小二乘问题代替原始问题．先由不精确牛顿法得到迭代方向，再沿着此方向回代使势函数下降，同时保证每一迭代点严格可行．证明了在合理的条件下具有整体收敛性和局部收敛速率．给出的数值结果表明了算法的有效性．

An affine scaling inexact Newton method with interior point backtracking technique for nonlinear problems subject to bounds on variables

We propose a new affine scaling inexact Newton method with interior point line search technique for solving the box constrained nonlinear optimization. Choosing the scaling matrices which have smoothness properties, we consider reformulated least squares with bounded constraints substituting the original problem. By the inexact Newton method we get a decreasing direction in each iterate. We also use line search along this decreasing direction to make the merit function adequately degressive and maintain strict feasibility. The algorithm is shown to be global and local convergent under some reasonable assumptions. The results of some numerical experiments are reported to show the effectiveness of the proposed algorithm.