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authorKarl Berry <karl@freefriends.org>2022-07-29 21:03:36 +0000
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-\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。