基于上方一致光滑逼近函数的高阶牛顿法求解线性规划

首先, 给出绝对值函数的3个上方一致光滑逼近函数的性质, 并用图像展示其逼近效果. 其次, 给出求解线性规划问题的一种新方法： 先把线性规划问题转化为非线性方程组, 然后采用一致光滑逼近函数得到光滑非线性方程组, 再利用高阶牛顿法进行求解. 数值实验结果表明, 该方法采用的上方一致光滑函数逼近程度优于目前已有算法, 在相同条件下计算耗时更少.

High Order Newton Method for Solving Linear ProgrammingBased on Uniform Smooth Approximation Function from Above#br#

Firstly, the author gave properties of three uniform smooth approximation functions for absolutevalue function from above, and demonstrated their approximationeffect with images. Secondly, a new method for solving linear programming problems was given.First, the linear programming problem was transformed into nonlinear equations, then the smooth nonlinear equations were obtained by uniform smooth approximation function, and then solved by high order Newton method. Numericalexperiments show that approximation degree of uniform smooth function from above adopted in this method is superior to the existing algorithms,and the computational time is less under the same conditions.