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研究生:何順進
研究生(外文):Shun-Chin Ho
論文名稱:廣義凸函數的最佳化與對偶定理
論文名稱(外文):Optimality and Duality with Generalized Convex Functions
指導教授:李金城李金城引用關係
指導教授(外文):Jin-Chirng Lee
學位類別:博士
校院名稱:中原大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2006
畢業學年度:95
語文別:英文
論文頁數:54
中文關鍵詞:Mond-Weir型的對偶問題參數型的對偶問題Wolfe型的對偶問題嚴格的反對偶定理
外文關鍵詞:strongstrict converse duality theoremweakparametric type dualMond-Weir type dualWolfe type dual
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在第一個部份,我們去處理分數型的多目標函數,討論它的有效解的必要條件與充份條件,
再利用那些條件去處理參數型的對偶問題,Wolfe型的對偶問題和Mond-Weir型的對偶問題,
並且證明它的一些對偶定理。
在第二各部份,在複數空間中處理極小大值的問題,得到了幾個充分條件的定理,在去討論參數型的對偶問題,
分別得到弱,強和嚴格的反對偶定理。
第三個部份,我們定義二階(F, )-凸函數,之後去討論Mond-Weir型的對偶問題,分別得到弱,強和嚴格的反對偶定理。
In part I, we establish necessary and sufficient conditions for efficiency of multiobjective
fractional programming problems involving r-invex functions. Using the optimality conditions,
we investigate the parametric type dual, Wolfe type dual and Mond-Weir type dual for multi-
objective fractional programming problems concerning r-invexity. Some duality theorems are
also proved for such problem in the framework of r-invexity.
In part II, we employ generalized convexity of complex functions to establish several suffi-
cient optimality conditions for minimax programming in complex spaces. Using such criteria,
we constitute a parametrical dual, and establish the weak, strong, and strict converse duality
theorems in the framework.
In part III, we establish weak, strong, and strict converse duality theorems for the general
second order Mond-Weir minimax dual problems containing generalized second order (F, )-
convex functions.
Part I
Optimality and Duality for Multiobjective Fractional Problems with r-invexity . . 1
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
1.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....3
2.Definitions and Preliminaries . . . . . . . . . . . . . . . . . . . . . . 3
3. Necessary and Sufficient Optimality Conditions . . . . . . . . . .. . . 5
4. Parametric Duality Model . . . . . . . . . . . . . . . . . . . . . . . . 9
5. Wolfe Type Dual Model . . . . . . . . . . . . . . . . . . . . . . . . . 15
6. Mond-Weir Duality. . . . . . . . . . . . . . . . . . . . . . . . . . . .19
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Part II
Parametric Duality on Minimax Programming Involving Generalized Convexity in
Complex Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2. Some Notations and Preliminary Results . . . . . . . . . . . . . . . . 30
3. Sufficient Optimality Conditions . . . . . . . . . . . . . . . . . . . 32
4. Parametric Duality Model . . . . . . . . . . . . . . . . . . .. . . . . 37
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Part III
Second Order (F, )-Convexity and Duality in Minimax Programming . . . . . 45
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
2. Notations and Preliminaries . . . . . . . . . . . . . . . . . . . . . . 47
3. Mond-Weir Duality. . . . . . . . . . . . . . . . . . . . . . . .. . . . 49
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
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