D.C.函數

D.C.Functions

林明仁(Ming-Jane Lin)

指導教授 ： 李金城

中原大學/理學院/應用數學系/碩士(2008年)

https://doi.org/10.6840/CYCU.2008.00017

摘要

摘要

此篇論文主要在討論D.C.函數。由Hiriart-Urruty, J.B.的著作(請參考﹝2﹞)發現有關於D.C.函數有下列五個方向可探討：
1. D.C.函數的基本性質
2. D.C.函數的特徵性質
3. 分解D.C.函數
4. 最佳化條件，D.C.函數的對偶
5. D.C.函數在最小值的應用

本文以探討D.C.函數的特徵性質為主題。先定義直線上的凸函數與有界變分函數，再進一步瞭解凸函數與有界變分函數的性質。最後，找到凸函數、有界變分函數與D.C.函數的關係。
關鍵字：
凸函數,凸分析,凸函數的差,有界變分函數。

關鍵字

凸函數的差 ； 凸函數 ； 有界變分函數。 ； 凸分析

並列摘要

Abstract

This thesis mainly discusses D.C. functions. In the opinion of J.B. Hiriart-Urruty﹝2﹞, there are five interesting problems concerning D.C. functions:
1. Basic properties of D.C. functions.
2. How to characterize a D.C. function?
3. How to decompose a D.C. function?
4. Optimality conditions, duality for D.C. function.
5. Preview on minimization procedures for D.C. functions.

The main purpose of this report is based on recognizing a D.C. function. After introducing the definitions of convex functions and functions of bounded variation on the real line, we investigate furtuer the characteristic of convex functions and functions of bounded variation. Then, we find the relationships among convex functions, function of bounded variation D.C. functions.

Key words:
convex function, convex analysis, D.C. function, function of bounded variation.

並列關鍵字

convex function ； function of bounded variation. ； convex analysis ； D.C. function

參考文獻

1.Ellaia, R. AND Hiriart-Urruty, J. B.: The Conjugate of the Difference of

Optimiyation for Problems Dealing With Differences of Convex Functions.

Lecture Wote in Ecouomics and Wath. Systems 256,37-70, 1986.

參考文獻

onvex Functions. J. of Optim. Theory and Appl, vol.49, no.3, 1986.