臺灣博碩士論文加值系統

近十年來，就線性互餘問題的研究分為兩大類；一類為路徑演算法
(path following method)，一類為潛能衰減演算法(potential
reduction method)。本篇論內容主要分為四部分，我們首先介紹使用路
徑演算法解線性互餘問題，包括其基本演算法則及其修正。在第二部分我
們描述使用潛能衰減演算法解線性互餘問題，包括使用長度技巧及斜率投
影技巧。第三部分包含一種新的方法，此法可解較線性互餘更為廣泛的問
題，且在以此法為基準的情形下，我們可以構造出路徑演算法或潛能衰減
演算法。線性互餘問題可整合線性規劃、二次目標函數規劃之問題及雙矩
陣遊戲之問題，此部分我們將最後說明。

In the last decade, work in linear complementarity problem
(LCP) can be distinguish into two classes; (1) path following
algorithm, and (2) potential reduction algorithm. The contents
of this paper are divided into four main parts. In the first
part we lay the path following algorithm for a LCP, including
its basic algorithm and modified algorithm. In the second part
we described the potential reduction algorithm for a LCP,
including the "norm" technique and the "gradient projection"
technique. The third part contains a "new" method which solves
more general problem than LCP. And we can construct a path
following method or a potential reduction method based on this
new method. The LCP is a general problem which unifies linear
and quadratic programs and bimatrix games are treated in the
last part.