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diff --git a/Master/texmf-dist/doc/xelatex/hithesis/back/appendix01.tex b/Master/texmf-dist/doc/xelatex/hithesis/back/appendix01.tex new file mode 100644 index 00000000000..26d53f3012e --- /dev/null +++ b/Master/texmf-dist/doc/xelatex/hithesis/back/appendix01.tex @@ -0,0 +1,247 @@ +\chapter{外文资料原文} +\label{cha:engorg} + +\title{The title of the English paper} + +\textbf{Abstract:} As one of the most widely used techniques in operations +research, \emph{ mathematical programming} is defined as a means of maximizing a +quantity known as \emph{bjective function}, subject to a set of constraints +represented by equations and inequalities. Some known subtopics of mathematical +programming are linear programming, nonlinear programming, multiobjective +programming, goal programming, dynamic programming, and multilevel +programming$^{[1]}$. + +It is impossible to cover in a single chapter every concept of mathematical +programming. This chapter introduces only the basic concepts and techniques of +mathematical programming such that readers gain an understanding of them +throughout the book$^{[2,3]}$. + + +\section{Single-Objective Programming} +The general form of single-objective programming (SOP) is written +as follows, +\begin{equation}\tag*{(123)} % 如果附录中的公式不想让它出现在公式索引中,那就请 + % 用 \tag*{xxxx} +\left\{\begin{array}{l} +\max \,\,f(x)\\[0.1 cm] +\mbox{subject to:} \\ [0.1 cm] +\qquad g_j(x)\le 0,\quad j=1,2,\cdots,p +\end{array}\right. +\end{equation} +which maximizes a real-valued function $f$ of +$x=(x_1,x_2,\cdots,x_n)$ subject to a set of constraints. + +\newtheorem{mpdef}{Definition}[chapter] +\begin{mpdef} +In SOP, we call $x$ a decision vector, and +$x_1,x_2,\cdots,x_n$ decision variables. The function +$f$ is called the objective function. The set +\begin{equation}\tag*{(456)} % 这里同理,其它不再一一指定。 +S=\left\{x\in\Re^n\bigm|g_j(x)\le 0,\,j=1,2,\cdots,p\right\} +\end{equation} +is called the feasible set. An element $x$ in $S$ is called a +feasible solution. +\end{mpdef} + +\newtheorem{mpdefop}[mpdef]{Definition} +\begin{mpdefop} +A feasible solution $x^*$ is called the optimal +solution of SOP if and only if +\begin{equation} +f(x^*)\ge f(x) +\end{equation} +for any feasible solution $x$. +\end{mpdefop} + +One of the outstanding contributions to mathematical programming was known as +the Kuhn-Tucker conditions\ref{eq:ktc}. In order to introduce them, let us give +some definitions. An inequality constraint $g_j(x)\le 0$ is said to be active at +a point $x^*$ if $g_j(x^*)=0$. A point $x^*$ satisfying $g_j(x^*)\le 0$ is said +to be regular if the gradient vectors $\nabla g_j(x)$ of all active constraints +are linearly independent. + +Let $x^*$ be a regular point of the constraints of SOP and assume that all the +functions $f(x)$ and $g_j(x),j=1,2,\cdots,p$ are differentiable. If $x^*$ is a +local optimal solution, then there exist Lagrange multipliers +$\lambda_j,j=1,2,\cdots,p$ such that the following Kuhn-Tucker conditions hold, +\begin{equation} +\label{eq:ktc} +\left\{\begin{array}{l} + \nabla f(x^*)-\sum\limits_{j=1}^p\lambda_j\nabla g_j(x^*)=0\\[0.3cm] + \lambda_jg_j(x^*)=0,\quad j=1,2,\cdots,p\\[0.2cm] + \lambda_j\ge 0,\quad j=1,2,\cdots,p. +\end{array}\right. +\end{equation} +If all the functions $f(x)$ and $g_j(x),j=1,2,\cdots,p$ are convex and +differentiable, and the point $x^*$ satisfies the Kuhn-Tucker conditions +(\ref{eq:ktc}), then it has been proved that the point $x^*$ is a global optimal +solution of SOP. + +\subsection{Linear Programming} +\label{sec:lp} + +If the functions $f(x),g_j(x),j=1,2,\cdots,p$ are all linear, then SOP is called +a {\em linear programming}. + +The feasible set of linear is always convex. A point $x$ is called an extreme +point of convex set $S$ if $x\in S$ and $x$ cannot be expressed as a convex +combination of two points in $S$. It has been shown that the optimal solution to +linear programming corresponds to an extreme point of its feasible set provided +that the feasible set $S$ is bounded. This fact is the basis of the {\em simplex + algorithm} which was developed by Dantzig as a very efficient method for +solving linear programming. +\begin{table}[ht] +\centering + \centering + \caption*{Table~1\hskip1em This is an example for manually numbered table, which + would not appear in the list of tables} + \label{tab:badtabular2} + \begin{tabular}[c]{|m{1.5cm}|c|c|c|c|c|c|}\hline + \multicolumn{2}{|c|}{Network Topology} & \# of nodes & + \multicolumn{3}{c|}{\# of clients} & Server \\\hline + GT-ITM & Waxman Transit-Stub & 600 & + \multirow{2}{2em}{2\%}& + \multirow{2}{2em}{10\%}& + \multirow{2}{2em}{50\%}& + \multirow{2}{1.2in}{Max. Connectivity}\\\cline{1-3} + \multicolumn{2}{|c|}{Inet-2.1} & 6000 & & & &\\\hline + & \multicolumn{2}{c|}{ABCDEF} &\multicolumn{4}{c|}{} \\\hline +\end{tabular} +\end{table} + +Roughly speaking, the simplex algorithm examines only the extreme points of the +feasible set, rather than all feasible points. At first, the simplex algorithm +selects an extreme point as the initial point. The successive extreme point is +selected so as to improve the objective function value. The procedure is +repeated until no improvement in objective function value can be made. The last +extreme point is the optimal solution. + +\subsection{Nonlinear Programming} + +If at least one of the functions $f(x),g_j(x),j=1,2,\cdots,p$ is nonlinear, then +SOP is called a {\em nonlinear programming}. + +A large number of classical optimization methods have been developed to treat +special-structural nonlinear programming based on the mathematical theory +concerned with analyzing the structure of problems. + +Now we consider a nonlinear programming which is confronted solely with +maximizing a real-valued function with domain $\Re^n$. Whether derivatives are +available or not, the usual strategy is first to select a point in $\Re^n$ which +is thought to be the most likely place where the maximum exists. If there is no +information available on which to base such a selection, a point is chosen at +random. From this first point an attempt is made to construct a sequence of +points, each of which yields an improved objective function value over its +predecessor. The next point to be added to the sequence is chosen by analyzing +the behavior of the function at the previous points. This construction continues +until some termination criterion is met. Methods based upon this strategy are +called {\em ascent methods}, which can be classified as {\em direct methods}, +{\em gradient methods}, and {\em Hessian methods} according to the information +about the behavior of objective function $f$. Direct methods require only that +the function can be evaluated at each point. Gradient methods require the +evaluation of first derivatives of $f$. Hessian methods require the evaluation +of second derivatives. In fact, there is no superior method for all +problems. The efficiency of a method is very much dependent upon the objective +function. + +\subsection{Integer Programming} + +{\em Integer programming} is a special mathematical programming in which all of +the variables are assumed to be only integer values. When there are not only +integer variables but also conventional continuous variables, we call it {\em + mixed integer programming}. If all the variables are assumed either 0 or 1, +then the problem is termed a {\em zero-one programming}. Although integer +programming can be solved by an {\em exhaustive enumeration} theoretically, it +is impractical to solve realistically sized integer programming problems. The +most successful algorithm so far found to solve integer programming is called +the {\em branch-and-bound enumeration} developed by Balas (1965) and Dakin +(1965). The other technique to integer programming is the {\em cutting plane + method} developed by Gomory (1959). + +\hfill\textit{Uncertain Programming\/}\quad(\textsl{BaoDing Liu, 2006.2}) + +\section*{References} +\noindent{\itshape NOTE: These references are only for demonstration. They are + not real citations in the original text.} + +\begin{translationbib} +\item Donald E. Knuth. The \TeX book. Addison-Wesley, 1984. ISBN: 0-201-13448-9 +\item Paul W. Abrahams, Karl Berry and Kathryn A. Hargreaves. \TeX\ for the + Impatient. Addison-Wesley, 1990. ISBN: 0-201-51375-7 +\item David Salomon. The advanced \TeX book. New York : Springer, 1995. ISBN:0-387-94556-3 +\end{translationbib} + +\chapter{外文资料的调研阅读报告或书面翻译} + +\title{英文资料的中文标题} + +{\heiti 摘要:} 本章为外文资料翻译内容。如果有摘要可以直接写上来,这部分好像没有 +明确的规定。 + +\section{单目标规划} +北冥有鱼,其名为鲲。鲲之大,不知其几千里也。化而为鸟,其名为鹏。鹏之背,不知其几 +千里也。怒而飞,其翼若垂天之云。是鸟也,海运则将徙于南冥。南冥者,天池也。 +\begin{equation}\tag*{(123)} + p(y|\mathbf{x}) = \frac{p(\mathbf{x},y)}{p(\mathbf{x})}= +\frac{p(\mathbf{x}|y)p(y)}{p(\mathbf{x})} +\end{equation} + +吾生也有涯,而知也无涯。以有涯随无涯,殆已!已而为知者,殆而已矣!为善无近名,为 +恶无近刑,缘督以为经,可以保身,可以全生,可以养亲,可以尽年。 + +\subsection{线性规划} +庖丁为文惠君解牛,手之所触,肩之所倚,足之所履,膝之所倚,砉然响然,奏刀騞然,莫 +不中音,合于桑林之舞,乃中经首之会。 +\begin{table}[ht] +\centering + \centering + \caption*{表~1\hskip1em 这是手动编号但不出现在索引中的一个表格例子} + \label{tab:badtabular3} + \begin{tabular}[c]{|m{1.5cm}|c|c|c|c|c|c|}\hline + \multicolumn{2}{|c|}{Network Topology} & \# of nodes & + \multicolumn{3}{c|}{\# of clients} & Server \\\hline + GT-ITM & Waxman Transit-Stub & 600 & + \multirow{2}{2em}{2\%}& + \multirow{2}{2em}{10\%}& + \multirow{2}{2em}{50\%}& + \multirow{2}{1.2in}{Max. Connectivity}\\\cline{1-3} + \multicolumn{2}{|c|}{Inet-2.1} & 6000 & & & &\\\hline + & \multicolumn{2}{c|}{ABCDEF} &\multicolumn{4}{c|}{} \\\hline +\end{tabular} +\end{table} + +文惠君曰:“嘻,善哉!技盖至此乎?”庖丁释刀对曰:“臣之所好者道也,进乎技矣。始臣之 +解牛之时,所见无非全牛者;三年之后,未尝见全牛也;方今之时,臣以神遇而不以目视, +官知止而神欲行。依乎天理,批大郤,导大窾,因其固然。技经肯綮之未尝,而况大坬乎! +良庖岁更刀,割也;族庖月更刀,折也;今臣之刀十九年矣,所解数千牛矣,而刀刃若新发 +于硎。彼节者有间而刀刃者无厚,以无厚入有间,恢恢乎其于游刃必有余地矣。是以十九年 +而刀刃若新发于硎。虽然,每至于族,吾见其难为,怵然为戒,视为止,行为迟,动刀甚微, +謋然已解,如土委地。提刀而立,为之而四顾,为之踌躇满志,善刀而藏之。” + +文惠君曰:“善哉!吾闻庖丁之言,得养生焉。” + + +\subsection{非线性规划} +孔子与柳下季为友,柳下季之弟名曰盗跖。盗跖从卒九千人,横行天下,侵暴诸侯。穴室枢 +户,驱人牛马,取人妇女。贪得忘亲,不顾父母兄弟,不祭先祖。所过之邑,大国守城,小 +国入保,万民苦之。孔子谓柳下季曰:“夫为人父者,必能诏其子;为人兄者,必能教其弟。 +若父不能诏其子,兄不能教其弟,则无贵父子兄弟之亲矣。今先生,世之才士也,弟为盗 +跖,为天下害,而弗能教也,丘窃为先生羞之。丘请为先生往说之。” + +柳下季曰:“先生言为人父者必能诏其子,为人兄者必能教其弟,若子不听父之诏,弟不受 +兄之教,虽今先生之辩,将奈之何哉?且跖之为人也,心如涌泉,意如飘风,强足以距敌, +辩足以饰非。顺其心则喜,逆其心则怒,易辱人以言。先生必无往。” + +孔子不听,颜回为驭,子贡为右,往见盗跖。 + +\subsection{整数规划} +盗跖乃方休卒徒大山之阳,脍人肝而餔之。孔子下车而前,见谒者曰:“鲁人孔丘,闻将军 +高义,敬再拜谒者。”谒者入通。盗跖闻之大怒,目如明星,发上指冠,曰:“此夫鲁国之 +巧伪人孔丘非邪?为我告之:尔作言造语,妄称文、武,冠枝木之冠,带死牛之胁,多辞缪 +说,不耕而食,不织而衣,摇唇鼓舌,擅生是非,以迷天下之主,使天下学士不反其本,妄 +作孝弟,而侥幸于封侯富贵者也。子之罪大极重,疾走归!不然,我将以子肝益昼餔之膳。” + + +\chapter{其它附录} +前面两个附录主要是给本科生做例子。其它附录的内容可以放到这里,当然如果你愿意,可 +以把这部分也放到独立的文件中,然后将其到主文件中。 |