臺灣博碩士論文加值系統

在本論文中，主要目的是探討非平滑集值函數的數值最佳化問題，我們使用Clarke 導數作為核心技術來研究集值函數的數值最佳解。進一步地，我們將所建構數值最佳化理論與方法，應用在動脈血管的動脈粥狀栓塞症的研究。在本文動脈血管疾病的研究，我們將非平滑集值函數視為動脈血管，以f+和f_之間的區域來描述，在非平滑的狹窄點的位置當作是粥狀動脈血管中的斑塊，以目標函數的Clarke導數方向當做主要媒介，使用數值疊代方法，有效求得粥狀動脈狹窄點的位置。

In this article, our main goal is to study the numerical optimization problem of the non-smooth set-valued mapping. We present a kernel technology for the convergence analysis of numerical optimization methods. Based on the concepts of the Clarke derivative and set-valued mappings. Moreover, the theory and the method of numerical analysis is applied to the study of an atherothrombosis. The non-smooth set-valued mapping is regarded as artery, denoted by the areas between f+ and f_, and the narrow non-smooth part is viewed as a plaque in an embolism artery. In numerical experiments, we use the Clarke derivatives of the object function as an effective tool to find the narrow point (minimizer) in an embolism artery.

Chinese abstract ………………………………………………………… I
Abstract ………………………………………………………………… II
Contents ……………………………………………………………...… III
Chapter 1 Introduction ………………………………………………… 1
Chapter 2 The Clarke tangent cone and the Clarke derivative in
set-valued mappings ……………………………………… 2
Chapter 3 Number Concepts and A Line Search Method …………... 10
Chapter 4 Implicit Filtering …………………………………………... 21
Chapter 5 Pattern Search Method ……………………………………. 36
Chapter 6 Numerical Computation of Implicit Filtering Method ….. 42
Chapter 7 Numerical Computation of A Pattern Search Method ..… 54
Chapter 8 Conclusions and Outlook ……………………………..…… 64
References ……………………………………………………………… 66
Appendix MATLAB Files ………………………………...…………… 68
Modified Implicit Filtering Version ………………………...………… 68
Simple Pattern Search Version ………………………………...……… 70

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