基于牛顿法及拟牛顿法的非线性规划算法改进及实证研究

The Improvement and Empirical Study of Nonlinear Programming Algorithm Based on Newton Method and Quasi-Newton Method

摘要: 非线性规划一直是优化理论研究的热点问题。本文将求解无约束非线性规划的三种常用方法(梯度法，牛顿法和拟牛顿法)进行对比分析，改进原有方法从而给出两种新算法，并说明改进算法的收敛性。在此基础上对基于竞争的配送中心选址问题进行了实证研究。

Abstract: Nonlinear programming has always been a hot topic in the research of optimization theory. In this paper, three commonly used methods for solving unconstrained nonlinear programming (gradient method, Newton method and quasi-Newton method) are compared and analyzed. Two new algorithms are given by improving the original method, and the convergence of the improved algorithm is illustrated. On this basis, this paper makes an empirical study on the location of distribution center based on competition.