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,主要是根據(jù)焦寶聰提出的廣義擬牛頓算法,對目標函數(shù)放寬了條件限制,結(jié)合goldstein線性搜索,對一般目標函數(shù)進行了收斂性的討論,其主要結(jié)果如下:全局收斂性定理若f ( x )在r ~ n上二次連續(xù)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 摘要本文將廣義互補問題轉(zhuǎn)化為一個非線性方程組問題,然后建立了gcp問題的無約束優(yōu)化問題的轉(zhuǎn)化形式,對該優(yōu)化問題,用兩種步長下的阻尼高斯牛頓算法來求解,并給出了兩種情況下算法的全局收斂性。
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 參數(shù)控制算法雖然與罰函數(shù)法非常類似,都是通過求解一系列無約束極小化問題來逼近約束優(yōu)化問題的最優(yōu)解,但罰函數(shù)法中的罰因子是預(yù)先設(shè)定的,而參數(shù)控制算法中的參數(shù)是自動產(chǎn)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 本文主要研究了共軛梯度法的算法和理論,得到了一些理論和數(shù)值結(jié)果。文中首先介紹共軛梯度法的發(fā)展概況,對幾種著名的共軛梯度法fr方法, prp方法, hs方法, cd方法和dy方法的全局收斂性,全局有效性及數(shù)值計算作了綜述。