【摘要】：共軛梯度法由于算法簡(jiǎn)單,易于編程.存儲(chǔ)需求少等特點(diǎn),常作為解決大規(guī)模非線性無(wú)約束優(yōu)化問(wèn)題的一種重要的方法,在現(xiàn)實(shí)生活的眾多領(lǐng)域頻繁使用且行之有效.本文首先介紹了經(jīng)典共軛梯度法,修正共軛梯度法,混合共軛梯度法,譜共軛梯度法的研究現(xiàn)狀.在前面學(xué)者研究成果的基礎(chǔ)之上,對(duì)共軛梯度法開(kāi)展了進(jìn)一步地分析和討論.得到以下研究成果:1.基于共軛梯度法的下降性條件,提出了一類充分下降的混合型譜共軛梯度法.該方法結(jié)合了 FR法,WYL法,PRP法的優(yōu)點(diǎn);然后,在Wolfe線搜索下用反證法證明了新的混合型譜共軛梯度法的全局收斂性.最后,通過(guò)數(shù)值算例,將算法WS與WYL法,FR法進(jìn)行比較,結(jié)果表明新算法在迭代次數(shù)與迭代總時(shí)間上均優(yōu)于其他另外兩種算法.算法的全局收斂性和數(shù)值效果的優(yōu)越性表明新算法是值得研究的.2.在修正共軛梯度法的基礎(chǔ)上,提出了一類WFR型譜共軛梯度法,該算法在任何線搜索下都具有充分下降性.在標(biāo)準(zhǔn)Wolfe線搜索下,證明了新算法具有全局收斂性.并對(duì)新算法進(jìn)行數(shù)值實(shí)驗(yàn),其實(shí)驗(yàn)結(jié)果表明新算法優(yōu)于VFR法。
[Abstract]:The conjugate gradient method is easy to program because of its simple algorithm. As an important method to solve large-scale nonlinear unconstrained optimization problems, it is often used frequently and effectively in many fields of real life. In this paper, the classical conjugate gradient method, the modified conjugate gradient method, the mixed conjugate gradient method and the spectral conjugate gradient method are introduced. Based on the previous research results, the conjugate gradient method is further analyzed and discussed. Get the following research results: 1. Based on the descent condition of conjugate gradient method, a class of mixed spectral conjugate gradient method with sufficient descent is proposed. This method combines the advantages of FR method and WYL method, and proves the global convergence of the new hybrid spectral conjugate gradient method under Wolfe line search. Finally, a numerical example is given to compare the WS algorithm with the WYL method. The results show that the new algorithm is superior to the other two algorithms in the number of iterations and the total iteration time. The global convergence of the algorithm and the superiority of numerical effect show that the new algorithm is worth studying. Based on the modified conjugate gradient method, a class of WFR type spectral conjugate gradient method is proposed, which has sufficient descent under any line search. Under the standard Wolfe line search, the global convergence of the new algorithm is proved. The experimental results show that the new algorithm is superior to the VFR method.
【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O224

【參考文獻(xiàn)】

相關(guān)期刊論文 前9條

1 馬文亞;;一類修正DY共軛梯度法及其全局收斂性[J];重慶工商大學(xué)學(xué)報(bào)(自然科學(xué)版);2015年05期

2 林穗華;黃海;;一個(gè)新的譜共軛梯度法[J];工程數(shù)學(xué)學(xué)報(bào);2014年06期

3 張雁;單銳;王換鵬;靳飛;;一類混合CD-LS共軛梯度法的全局收斂性[J];遼寧工程技術(shù)大學(xué)學(xué)報(bào)(自然科學(xué)版);2013年03期

4 黃海;林穗華;;一個(gè)PRP型共軛梯度法的收斂性[J];西南大學(xué)學(xué)報(bào)(自然科學(xué)版);2012年03期

5 江羨珍;韓麟;簡(jiǎn)金寶;;Wolfe線搜索下一個(gè)全局收斂的混合共軛梯度法[J];計(jì)算數(shù)學(xué);2012年01期

6 李燦;;修正FR共軛梯度法的全局收斂性[J];西北師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2011年05期

7 ;Global Convergence of a Modified Spectral CD Conjugate Gradient Method[J];數(shù)學(xué)研究與評(píng)論;2011年02期

8 王開(kāi)榮;曹偉;王銀河;;Armijo型線搜索下的譜CD共軛梯度法[J];山東大學(xué)學(xué)報(bào)(理學(xué)版);2010年11期

9 ;GLOBAL CONVERCENCE OF THE FLETCHER-REEVES ALGORITHM WITH INEXACT LINESEARCH[J];Applied Mathematics:A Journal of Chinese Universities(Series B);1995年01期

相關(guān)碩士學(xué)位論文 前1條

1 吳偉霞;幾種含參數(shù)的共軛梯度法的全局收斂性研究[D];重慶大學(xué);2008年

，

本文編號(hào)：2218960