复共轭梯度法的结构  

Structure of the Complex Conjugate Gradient Method

作　　者：魏志强[1] 张愿章[1] 

机构地区：[1]华北水利水电学院数学与信息科学学院,河南郑州450011

出　　处：《哈尔滨理工大学学报》2012年第4期122-126,共5页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11101145);河南省基础与前沿技术研究计划项目(102300410129)

摘　　要：从复问题本身出发,对实值复变函数的优化问题引入了最优复搜索的概念,得到了最优复搜索的条件.给出并证明了二次优化问题的复共轭方向法与复共轭梯度法,并藉此给出了一般实值复变函数优化问题的复共轭梯度法.对复问题的直接推导与证明明晰了复共轭梯度法的数学结构.复共轭梯度法可以理解为是在实共轭梯度法中直接将实转置改为共轭转置得到的.In the complex domain, the conception of optimal complex-search was defined for the optimization problems of real-valued complex function and the necessary condition of optimal complex-search is obtained. The complex conjugate direction method and the complex conjugate gradient methods are proposed for the quadratic optimization. Moreover, the complex conjugate gradient methods for the optimization problems of general real-valued complex function are given. The structure of the complex conjugate gradient method is clear through the direct deduction and proof of complex problems. The complex conjugate gradient method can be viewed as the real conjugate gradient method that its real matrix transpose replaced by matrix conjugate transpose.

关 键 词：复域优化问题 复共轭方向法 复共轭梯度法 

分 类 号：O224[理学—运筹学与控制论]