求解线性规划问题的光滑型牛顿算法

Smoothing Newton algorithm for solving linear programs problem

对线性规划的最优性条件,给出一个扩展系统,设计一个连续化的光滑型算法求解该系统。所设计的算法的全局收敛性不需要添加任何假设条件。在每一个迭代点处,只需要解一个线性方程组和做一次线性搜索,比现有求解线性规划问题的连续化方法具有更好的收敛性质。

We propose a continuation method for solving the Linear Program （LP） by making use of an augmented system of its optimality conditions.The algorithm is shown to be globally convergent without requiting any assumption.It only needs to solve one system of linear equations and to perform one line search at each iteration.To the best of our knowledge this is the first continuation smoothing-type algorithm for solving the LP having the above desired convergence features.