一种修正的三项PRP共轭梯度法  

A modified three terms PRP conjugate gradient method

作　　者：王松华 黎勇 吴加其 陆乃畅 WANG Songhua;LI Yong;WU Jiaqi;LU Naichang(School of Mathematics and Statistics,Baise University,Baise,Guangxi533000,China;College of Mathematics and Information Science,Guangxi University,Nanning,Guangxi530004,China;University of Michigan-Ann Arbor,Ann Arbor,Michigan48104,USA)

机构地区：[1]百色学院数学与统计学院,广西百色533000 [2]广西大学数学与信息科学学院,广西南宁530004 [3]密西根大学安娜堡分校,美国密西根安娜堡48104

出　　处：《河北科技大学学报》2018年第6期518-526,共9页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金(11661009);广西省自然科学青年基金项目(2014GXNSFBA118283);广西省教育厅科研项目(YB2014389;YB2014381)

摘　　要：为了更有效求解一类大规模无约束优化问题,克服其他算法普遍存在的算法较为复杂,存储量大和计算机编程难等不足,在传统三项PRP共轭梯度法的基础上,结合近年来关于三项共轭梯度法和新型线搜索的研究成果,定义了一种新的搜索方向,并采用一种新型的线搜索构建了算法,证明了其具有自动充分下降和信赖域的性质,并在适当的条件下证明了其全局收敛性。数值试验结果表明,在求解一类大规模无约束优化问题上新算法比传统三项PRP共轭梯度法更具有竞争性。具有良好收敛性质的新算法为解决一类求解大规模无约束优化问题提供了更高效的算法依据。In order to effectively solve a class of large-scale unconstrained optimization problems and overcome the shortcomings of other algorithms,such as complex algorithms,large memory and computer programming difficulties,a new search direction is defined,which is based on some traditional three terms PRP conjugate gradient methods as well as combined with the research results of three terms conjugate gradient and some new line searches in recent years.A new line search algorithm is used to construct the algorithm,which proves that it has the properties of automatic full descent and trust region,and proves its global convergence under appropriate conditions.Numerical experiments has showed that the new algorithm is more competitive than the traditional three-term PRP conjugate gradient method in solving a class of large-scale unconstrained optimization problems.The new algorithm with better convergence property provides a more efficient algorithm basis for solving a class of large-scale unconstrained optimization problems.

关 键 词：最优化 无约束优化 共轭梯度法 充分下降性 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]