In this paper , a class of algorithms which are update quasi - newton methods for unconstrained optimization as follows : this article consists , of three parts . the first part is the introduction of the quasi - newton methods for unconstrained optimization . the second part is the proof of the global and superlin - early convergence of the generalized - quasi - newton methods . the third part is quasi - newton - non - convex class methods and its global convergence . the main results of the second part are as follows : theorem of global convergence 在第一章中,主要是根据焦宝聪提出的广义拟牛顿算法,对目标函数放宽了条件限制,结合goldstein线性搜索,对一般目标函数进行了收敛性的讨论,其主要结果如下:全局收敛性定理若f ( x )在r ~ n上二次连续可微,有下界,水平集。
In this paper we reformulate gcp a sasystem of nonlinear equations , and the gcp is reformulated as unconstrained optimization problem , as for the optimization problem , the damped gauss - newton method algorithm of two kinds of steps is employed for obtaining its solution , and the global convergence analysis are given in this thesis 摘要本文将广义互补问题转化为一个非线性方程组问题,然后建立了gcp问题的无约束优化问题的转化形式,对该优化问题,用两种步长下的阻尼高斯牛顿算法来求解,并给出了两种情况下算法的全局收敛性。
The parameter control methods are very similar to penalty function methods , both of them are to solve constrained optimization problems by solving a series of sub - unconstrained optimization problems . but parameter control methods are different from penalty function methods . firstly , the penalty coefficient of penalty function methods are preassigned , while the parameters of parameter control methodsare generated automatically according to some rule prescribed 参数控制算法虽然与罚函数法非常类似,都是通过求解一系列无约束极小化问题来逼近约束优化问题的最优解,但罚函数法中的罚因子是预先设定的,而参数控制算法中的参数是自动产生的。
In this thesis , we mainly discuss the algorithm and the theory of conjugate gradient method . the structure of this paper is organized as follows : in the first chapter we survey the history of conjugate gradient method , and discuss five conjugate gradient methods respectively which are fr method , prp method , hs method , cd method , dy method . they are currently considered to be well - known methods for large scale unconstrained optimization problems 本文主要研究了共轭梯度法的算法和理论,得到了一些理论和数值结果。文中首先介绍共轭梯度法的发展概况,对几种著名的共轭梯度法fr方法, prp方法, hs方法, cd方法和dy方法的全局收敛性,全局有效性及数值计算作了综述。