臺灣博碩士論文加值系統

在這篇論文中，我們討論在強單調算子或反強單調算子下，單調變分不等式的存在收斂結果。我們將變分不等式問題等價於固定點問題以公式表示之，並使用固定點疊代法去解決原使變分不等式的問題。
在強單調的部分：我們使用 Banach’s 壓縮原理定義疊代序列；在反強單調的部分：我們使用平均映像的技巧定義疊代序列，在這兩部分我們都利用疊代法證明是強收斂，最後應用於解決最小值的問題。

In this paper, we report existing convergence results on monotone variational inequalities where the governing monotone operators are either strongly monotone or inverse strongly monotone. We reformulate the variational inequality problem as
an equivalent fixed point problem and then use fixed point iteration method to solve the original variational inequality problem. In the case of strong monotonicity case we use the Banach’s contraction principle to define out iteration sequence; while in the case of inverse strong monotonicity we use the technique of averaged mappings to define our iteration sequence. In both cases we prove strong convergence for our
iteration methods. An application to a minimization problem is also included.

1 Introduction
2 Fixed Point Theorems
3 VI(F,C) Where F Is Strongly Monotone
4 VI(F,C) Where F Is Inverse Strongly Monotone
5 An Application in Optimization
6 References

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