臺灣博碩士論文加值系統

在這篇文章中, 我們所要解決的問題是有界線性規劃問題. 此線性規
劃問題每一個變數的上界, 下界可以是有值的或是正負無限大,因此, 我
們所要處裡的變數有自由變數, 一邊有界或者是兩邊皆有界的變數. 在作
法上, 我們利用壁壘函數( barrier function )造一個內部點演算法來解
決此一問題. 接著, 我們說明如何尋找此演算法的起始點. 最後, 我們利
用兩個典型的例子來執行此演算法, 並比較兩個不同壁壘函數的執行成
果. 關於此篇文章的第二章及第三章的內容, 是參考Freund和Todd[1]
的內容.

In this paper, we consider a linear programming problem with
boundson variables. These upper bounds and lower bounds of the
variables forthis linear programming problem can be nonfinite.
Thus, the variablescan be free, 1-sided or 2-sided bounded. In
this paper, we first introduce an algorithm proposed by Freund
and Todd in 1995 to solve this problems. Then we introduce how
to get a starting point of thisalgorithm. Finally, we implement
the algorithm with two numerical examples and compare the
behavior of the algorithm with two barrier functions.