本文選題：全局優(yōu)化　切入點(diǎn)：局部極小點(diǎn)　出處：《重慶大學(xué)》2016年碩士論文

【摘要】：最優(yōu)化在實(shí)際生活中普遍存在,它是一個應(yīng)用非常廣泛的數(shù)學(xué)分支,隨著科技的發(fā)展和社會的進(jìn)步,最優(yōu)化在工程設(shè)計、交通運(yùn)輸、生產(chǎn)管理、經(jīng)濟(jì)計劃等方面都有著很大量的運(yùn)用。全局優(yōu)化問題主要有兩個困難:一是怎樣自通過局部優(yōu)化已經(jīng)得到的一個局部極小解去尋找更加優(yōu)的局部極小解;二是如何判斷目前的局部極小解是全局極小解。全局優(yōu)化大致分為兩個類型:一是確定性算法;二是隨機(jī)性算法。其中,填充函數(shù)法是一種非常有效的第一類型的算法,它最先是由Ge[23]提出的,主要是解決上面提到的第一個困難。它的根本思想是在通過局部優(yōu)化得到的局部極小點(diǎn)處構(gòu)造一個關(guān)于目標(biāo)函數(shù)的復(fù)合函數(shù),稱之為填充函數(shù),利用該復(fù)合函數(shù)使目標(biāo)函數(shù)離開目前的局部極小點(diǎn),從而找到更加優(yōu)的局部極小點(diǎn)。填充函數(shù)法借助了局部極小化算法,而局部優(yōu)化理論和算法都發(fā)展的相當(dāng)完善,于是填充函數(shù)法得到了廣大最優(yōu)化研究者的推崇,其算法關(guān)鍵在于填充函數(shù)的構(gòu)造。全文分為五章:第一章簡單地闡述了研究最優(yōu)化以及非光滑優(yōu)化重要性,然后給出了最優(yōu)化方面本文需要的相關(guān)的基礎(chǔ)定義,之后詳細(xì)說明了在全局優(yōu)化問題當(dāng)中,填充函數(shù)法的產(chǎn)生背景和發(fā)展前景,并分析了學(xué)者們提出的填充函數(shù)的優(yōu)缺點(diǎn)。第二章在無約束優(yōu)化問題中,根據(jù)文獻(xiàn)[46]給出的經(jīng)典的填充函數(shù)的定義,給出了一個連續(xù)可微的單參數(shù)填充函數(shù),克服了文獻(xiàn)[23,46,70]中的填充函數(shù)出現(xiàn)指數(shù)項(xiàng)和文獻(xiàn)[59,72,73]中填充函數(shù)在*f(x)?f(x)時不出現(xiàn)目標(biāo)函數(shù)的任何信息的缺點(diǎn)。第三章根據(jù)文獻(xiàn)[71]給定的有別于經(jīng)典定義[46]的一種新的有效定義,在該新的定義上提出了一個新的單參數(shù)填充函數(shù),另外克服了文獻(xiàn)[71]中的函數(shù)在)()(*xfxf?時是不連續(xù)的缺陷。第四章首先給出了非光滑優(yōu)化方面的一些基礎(chǔ)知識,在非光滑無約束全局優(yōu)化中,構(gòu)造了一個雙參數(shù)填充函數(shù),實(shí)際上該函數(shù)可以視為單參數(shù),相比文獻(xiàn)[69],該函數(shù)得到了一定的改善,填充函數(shù)沒有指數(shù)項(xiàng)。第五章對本文做了總結(jié)并對展望了填充函數(shù)法的發(fā)展。
[Abstract]:Optimization is a widely used branch of mathematics in real life. With the development of science and technology and social progress, optimization in engineering design, transportation, production management, The global optimization problem has two main difficulties: one is how to find a more optimal local minima solution by means of a local minima solution that has been obtained by local optimization; The second is how to judge that the local minima is a global minima. The global optimization can be divided into two types: one is deterministic algorithm, the other is randomness algorithm, in which the fill function method is a very effective first type algorithm. It was first put forward by GE [23], mainly to solve the first difficulty mentioned above. Its basic idea is to construct a compound function about the objective function at the local minima obtained by local optimization, which is called filling function. The compound function is used to make the objective function leave the current local minima, thus finding a more optimal local minima. The filling function method uses the local minimization algorithm, and the local optimization theory and algorithm are developed perfectly. Therefore, the filling function method is highly praised by the majority of optimization researchers, and the key of its algorithm lies in the construction of the filling function. The paper is divided into five chapters: chapter one simply describes the importance of studying optimization and non-smooth optimization. Then it gives the basic definition of optimization in this paper, and then explains the background and development prospect of the filling function method in the global optimization problem in detail. The advantages and disadvantages of the filling function proposed by scholars are analyzed. In the second chapter, according to the classical definition of filling function given in [46], a continuous differentiable single parameter filling function is given in the unconstrained optimization problem. It overcomes the occurrence of exponential term in the filling function in [23] and the filling function in [59 ~ 722 ~ (73)]. In chapter 3, according to a new effective definition given in reference [71], different from the classical definition [46], a new one-parameter filling function is proposed in this new definition. In addition, it overcomes the function in [71]. In chapter 4, we first give some basic knowledge of non-smooth optimization. In non-smooth unconstrained global optimization, we construct a two-parameter filling function. In fact, this function can be regarded as a single parameter. Compared with the reference [69], this function has been improved, and the filling function has no exponential term. In Chapter 5, the author summarizes this paper and looks forward to the development of the filling function method.
【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O224

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