在第一章我先介紹有關有限線性規劃的一些基本性質。接著我將這些基本性質推廣到無限和半無限線性規劃。進一步我比較這些基本性質在有限線性規劃和無限和半無限線性規劃的差異。同時我給一些實際問題並將他們表示成無限和半無限線性規劃問題。最後，我討論有限二次規劃、無限二次規劃和半無限二次規劃。
在第二章我考慮半無限運輸問題。我發展一個演算法來處理這類型的半無限運輸問題。這個演算法是一個對偶單形法。我的重要結果是證明這個演算法是收斂。最後，我用我的演算法來處理一些例子。
在第三章我研究無限二次規劃問題。我考慮的變數要落在Lp空間，而且要求變數定義在一個緊緻區間同時要有上界和下界。我發展兩個演算法來解決這類型問題同時也證明這兩個演算法是收斂的。最後，我應用我的演算法來解一些數值例子。
在第四章我對半無限運輸問題和無限二次規劃問題作一些結論。

In Chapter 1, first, we introduce some basic properties for finite linear pro-
gramming. Then we extend these basic properties to infinite and semi-infinite
linear programming. Furthermore, we compare the differences of these ba-
sic properties between finite linear programming and infinite and semi-infinite
linear programming. We also give some natural problems and express them
as infinite and semi-infinite linear programming. In the final section, we dis-
cuss finite quadratic programming, infinite quadratic programming, and semi-
infinite quadratic programming.
We consider semi-infinite transportation problems in Chapter 2. We de-
velop an algorithm for this class of semi-infinite transportation problems. The
algorithm is a dual simplex method which is induced from the algorithm in An-
derson and Nash [3] for a special class of semi-infinite transportation problems.
The most important aspect of our result is that we can prove the convergence
result for the algorithm. Finally, we implement some examples to illustrate
our algorithm.
We study infinite dimensional quadratic programming problems of an in-
tegral type in Chapter 3. The decision variable is taken in the Lp space.
In this chapter the decision variable is required to have a lower
bound and an upper bound on a compact interval. Two numerical algorithms
are proposed for solving these problems, and the convergence properties of the
proposed algorithms are given. Some numerical examples are also given to
implement the proposed algorithms.
In Chapter 4, we make some conclusions about semi-infinite transportation
problems and infinite quadratic programming problems.

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