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--- a/macros/latex/contrib/hitszthesis/back/appendix02.tex
+++ b/macros/latex/contrib/hitszthesis/back/appendix02.tex
@@ -1,32 +1,104 @@
% !TEX root = ../main.tex
% 附录2
-\chapter{外文资料的调研阅读报告或书面翻译}
+\chapter{外文资料原文}
+\label{cha:engorg}
-\title{英文资料的中文标题}
+\title{The title of the English paper}
-{\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。
+\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$^{[1]}$.
-\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})}
+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.
-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。
+\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}
-\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。
+\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*{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}
+ \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
@@ -40,33 +112,64 @@
\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。”
+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.
-文惠君曰:“善哉!吾闻庖丁之言,得养生焉。”
+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}
-\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。”
+{\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).
-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。”
+\hfill\textit{Uncertain Programming\/}\quad(\textsl{BaoDing Liu, 2006.2})
-孔子不听,颜回为驭,子贡为右,往见盗跖。
+\section*{References}
+\noindent{\itshape NOTE: These references are only for demonstration. They are
+ not real citations in the original text.}
-\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。”
+\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}