无约束最优化问题的非线性共轭梯度算法的研究

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1、4.1混合共轭梯度算法····················································································334.2全局收敛性的分析····················································································344.3实例分析················································································

2、····················384.4小结·············································································································39第5章基于非线性共轭梯度法的条件异方差时间序列的建模与应用···415.1ARCH模型·································································································41

3、5.2GARCH模型·····························································································41 5.2.1GARCH模型的约束条件··································································42 5.2.2AR(m)-GARCH模型·······································································

4、··42 5.3GARCH(p,q)模型的建模思想·································································43 5.4实例分析····································································································435.5小结··········································································

5、···································47结论·························································································································49 参考文献·················································································································5

6、1 攻读硕士学位期间承担的科研任务与主要成果············································55 致谢·························································································································56 作者简介··················································································

7、·······························57万方数据第1章绪论4.1引言共轭梯度法是最优化中最常用的方法之一。在所有需要计算导数的优化方法中，最速下降法是最简单的，但它速度太慢。拟牛顿方法收敛速度很快，被广泛认为是非线性规划的最有效的方法。但拟牛顿方法需要存储矩阵以及通过求解线性方程组来计算搜索方向，这对大规模问题几乎是不可能办到的。而共轭梯度法算法简便，存储需求小，收敛速度又比最速下降法快，特别适合求解大规模问题。在石油勘探、大气模拟、航天航空等领域出现的大规模问题常常是利用共轭梯度法来求解的。考虑如下气象学中的一个例子，它是讲述如

8、何用四维变分同化方法从大量已知数据中有效地决定大气的初始状态，从而