【摘要】：極大值方程問(wèn)題是非光滑方程問(wèn)題中一類(lèi)很重要的問(wèn)題,經(jīng)常被用于求解非線(xiàn)性互補(bǔ)、變分不等式和工程力學(xué)等問(wèn)題,并廣泛應(yīng)用于圖像存儲(chǔ)、隨機(jī)均衡及優(yōu)化控制等問(wèn)題的研究。本文主要對(duì)極大值方程問(wèn)題的求解算法及其應(yīng)用進(jìn)行了研究。第一章對(duì)極大值方程問(wèn)題的相關(guān)知識(shí)做了簡(jiǎn)單介紹,其中包括問(wèn)題的來(lái)源、發(fā)展情況等,并介紹了極大值方程的應(yīng)用。第二章給出了求解極大值方程問(wèn)題的一種參數(shù)組合牛頓法,此算法主要借助于一種新的微分形式,在一般的假設(shè)條件下,證明了算法的局部超線(xiàn)性收斂結(jié)果,最后給出了相關(guān)的數(shù)值實(shí)驗(yàn)表明了算法的有效性。第三章給出了求解極大值方程問(wèn)題的改進(jìn)參數(shù)組合牛頓法,克服了在算法中要求矩陣kV非奇異的限制,證明了算法的局部超線(xiàn)性收斂性,并給出了相關(guān)的數(shù)值實(shí)驗(yàn)。第四章對(duì)一類(lèi)廣義互補(bǔ)問(wèn)題進(jìn)行了轉(zhuǎn)化,將其轉(zhuǎn)化為極大值方程問(wèn)題,并且利用給出的參數(shù)組合牛頓法對(duì)其進(jìn)行了求解。
[Abstract]:Maxima equation problem is a very important problem in non-smooth equation problem. It is often used to solve nonlinear complementarity, variational inequality and engineering mechanics, and is widely used in image storage. Study on stochastic equilibrium and optimal control. In this paper, the algorithm and its application of the problem of maximum equation are studied. In the first chapter, we briefly introduce the knowledge about the problem of the maximum equation, including the origin and development of the problem, and introduce the application of the maximum equation. In the second chapter, a parameter combination Newton method is given to solve the maximum value equation problem. This method is mainly based on a new differential form. Under general assumptions, the local superlinear convergence results of the algorithm are proved. Finally, relevant numerical experiments are given to show the effectiveness of the algorithm. In chapter 3, an improved parameter combination Newton method for solving the problem of maximum equation is given, which overcomes the limitation of matrix kV nonsingularity in the algorithm, proves the local superlinear convergence of the algorithm, and gives the relevant numerical experiments. In chapter 4, a class of generalized complementarity problem is transformed into a maximum value equation problem, and it is solved by using the given parameter combination Newton method.
【學(xué)位授予單位】：青島大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O241.8

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