【作者】 田凤婷；

【导师】 孙清滢；

【作者基本信息】 中国石油大学 ， 数学， 2010， 硕士

【摘要】 本文主要研究求解无约束优化问题的拟牛顿算法,提出了三个新的拟牛顿算法.主要内容如下:第二章基于新拟牛顿方程,结合BFGS类修正公式构造了一个新的拟牛顿算法,在一定假设条件下,证明了算法的全局收敛性质和算法的超线性收敛速度.数值试验结果表明算法是有效的.第三章基于拟牛顿方程,结合非单调线搜索技术,设计了求解无约束最优化问题的改进Grippo非单调线搜索规则的新的对角稀疏拟牛顿算法,证明了算法的全局收敛性和算法的超线性收敛速度.新的步长规则在每一次线搜索时得到一个相对于Grippo非单调线搜索规则的较大步长,同时保证算法的全局收敛性.数值试验表明算法是有效的,适合求解大规模问题.第四章基于广义拟牛顿方程,结合改进的非单调线搜索技术,设计了求解无约束最优化问题的改进Grippo非单调线搜索规则的新的对角稀疏广义拟牛顿算法,证明了算法的全局收敛性和算法的超线性收敛速度.数值试验表明算法是有效的,适合求解大规模问题.更多还原

【Abstract】 In this paper, we propose three new quasi-Newton methods for unconstrained optimization. The main content of the thesis is presented as follows:In chapter two, based on new quasi-Newton equation, we propose new quasi-Newton method combining with BFGS-type update formula. Under some assumptions, we proved the global convergence and the speed of super linear convergence. Numerical results show that the method is effective.In chapter three, based on the quasi-Newton equation, together with non–monotone line search skill, we designed a new diagonal-sparse quasi-Newton method with modified Grippo non-monotone line search for unconstrained optimization. The global convergence and super linear convergence are guaranteed to our new method, meanwhile, in every iteration, the new step size generated by the new method is lager than that of Grippo non-monotone line search. Numerical experiments show that the new method is effective and suitable for large scale problems.In chapter four, on the base of new quasi-Newton equation, together with modified non-monotone line search skill, we designed new diagonal-sparse modified quasi-Newton method with modified Grippo non-monotone line search for unconstrained optimization. Global convergence and super linear convergent speed of the method are proved. Numerical experiments show that the new method is effective and suitable for large scale problems.更多还原