有限多個(gè)變分不等式的一般迭代法及在優(yōu)化中的應(yīng)用
發(fā)布時(shí)間：2018-08-27 05:44
【摘要】：本文在實(shí)Hilbert空間中引入了某個(gè)優(yōu)化問(wèn)題的一般迭代法,此優(yōu)化問(wèn)題的約束集是關(guān)于連續(xù)單調(diào)映像的有限多個(gè)變分不等式問(wèn)題的解集、有限多個(gè)變分包含問(wèn)題的解集和一個(gè)連續(xù)偽壓縮映像的不動(dòng)點(diǎn)集之交集.本文主要分為四部分,下面我們逐一來(lái)介紹.第一章,主要介紹了變分不等式理論的研究簡(jiǎn)況和本文的主要工作.第二章,給出了所建議的隱式迭代算法及其性質(zhì).第三章,在適當(dāng)?shù)目刂茥l件下,依據(jù)隱式迭代法的性質(zhì),證明了該方法強(qiáng)收斂到交集中的一個(gè)元,該元是某個(gè)優(yōu)化問(wèn)題的唯一解.由此即得,該方法強(qiáng)收斂到交集中唯一的范數(shù)最小元.第四章,介紹了同樣也能夠建立顯式迭代法,并給出了顯式迭代法的收斂性分析結(jié)果.本文結(jié)果是對(duì)已有結(jié)果的改進(jìn)和推廣.
[Abstract]:In this paper, we introduce a general iterative method for an optimization problem in real Hilbert spaces. The constrained set of the optimization problem is the solution set of finite variational inequalities for continuous monotone mapping. The intersection of the solution set of finite variational inclusions and the fixed point set of a continuous pseudo contractive mapping. This article is mainly divided into four parts, below we introduce one by one. In the first chapter, the research situation of variational inequality theory and the main work of this paper are introduced. In chapter 2, the proposed implicit iterative algorithm and its properties are given. In chapter 3, under appropriate control conditions, according to the properties of implicit iterative method, it is proved that the method converges strongly to an element in the intersection, which is the unique solution of an optimization problem. It is obtained that the method converges strongly to the unique norm minimum element in the intersection. In chapter 4, the explicit iterative method is also introduced, and the convergence analysis results of the explicit iterative method are given. The results in this paper improve and generalize the existing results.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O177.91
本文編號(hào)：2206260
[Abstract]:In this paper, we introduce a general iterative method for an optimization problem in real Hilbert spaces. The constrained set of the optimization problem is the solution set of finite variational inequalities for continuous monotone mapping. The intersection of the solution set of finite variational inclusions and the fixed point set of a continuous pseudo contractive mapping. This article is mainly divided into four parts, below we introduce one by one. In the first chapter, the research situation of variational inequality theory and the main work of this paper are introduced. In chapter 2, the proposed implicit iterative algorithm and its properties are given. In chapter 3, under appropriate control conditions, according to the properties of implicit iterative method, it is proved that the method converges strongly to an element in the intersection, which is the unique solution of an optimization problem. It is obtained that the method converges strongly to the unique norm minimum element in the intersection. In chapter 4, the explicit iterative method is also introduced, and the convergence analysis results of the explicit iterative method are given. The results in this paper improve and generalize the existing results.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O177.91
【參考文獻(xiàn)】
相關(guān)期刊論文 前1條
1 張石生;李向榮;陳志堅(jiān);;Algorithms of common solutions to quasi variational inclusion and fixed point problems[J];Applied Mathematics and Mechanics(English Edition);2008年05期
，本文編號(hào)：2206260
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