文档介绍：广西大学硕士学位论文一类修改的信赖域算法姓名:周亚群申请学位级别:硕士专业:运筹学与控制论指导教师:韦增欣 20070526 一类修改的信赖域算法摘要信赖域方法是近二十年来发展起来的一类重要的数值计算方法。由于具有很好的可靠性、强适性,以及很强的收敛性,目前它和传统的的线搜索方法并列为求解非线性规划的两类主要的数值计算方法。本文主要研究一个修改的BFGS公式在信赖域方法中的应用,其结构如下: 第一章,回顾了信赖域算法的基本思想和研究状况,根据韦增欣等给出的新的拟牛顿方程,给出了一个新的BFGS校正公式,并分析了相关性质。第二章,结合新的校正公式,我们提出一种求解无约束优化问题的非单调的BFGS信赖域方法,并证明该方法求解非凸极小化问题的全局收敛性。该算法的优点是信赖域子问题的目标函数是一个严格凸二次函数,因而信赖域子问题的求解相对容易。而且,我们在不假设迭代矩阵序列有界的前提下建立算法的全局收敛性定理。第三章,将修改的BFGS公式与ArmUo线搜索相结合,得到一个新的信赖域算法。在适当条件下,证明了该算法具有全局收敛性和超线性收敛性。数值结果表明此算法对无约束优化问题是有效的。关键词:BFGS方法信赖域方法线搜索全局收敛性超线性收敛性 ACLASS oF MODIFIED TRUST REGIoN METHoDS ABSTRACT Trust region method is an important numerical method developed OVer the lasttwo ofitsreliability,robustness and strong convergence,trust region method, together with linesearchmethod,has e one ofthe two main numerical methods for solving nonlinear mainly discuss theapplication of amodified BFGS formula anized as follows: InChapter review thebasicthought and research ofthe trustreglon method. According tothe new quasi Newton equation proposed byWei atal。we give anewmodified BFGS formulaandanalyze thecorresponding properties. InChapter2,corresponding tOthenew formula,we develop anonmonotOne BFGS trust-region method forsolving unconstrained optimization goodproperty ofthe method isthat theobjective function of thetrust-region subproblem is astrictlyconvex quadratic ,it isrelativelyeasy tOsolve establish a globalconvergence theorem forthemethod without requirement ofthe boundedness ofthe generated matrix sequence. InChapter bining the modified BFGS formula witllarmijo linesearch,we propose anew trustregion method,and prove thatthealgorithms are globalandsuperlinear convergence under some numerical results show thatthemethod isefficientand advisable fornonlinear optimization. KEY WORDS..BFGS method;Trust regionmethod;Line search:Global convergence; Superlinear convergence 符