廣義凸函數的最佳化與對偶定理

Optimality and Duality with Generalized Convex Functions

何順進(Shun-Chin Ho)

指導教授 ： 李金城

中原大學/理學院/數學研究所/博士(2007年)

https://doi.org/10.6840/CYCU.2007.00002

摘要

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。

關鍵字

Mond-Weir型的對偶問題 ； 參數型的對偶問題 ； 強 ； Wolfe型的對偶問題 ； 弱 ； 嚴格的反對偶定理

並列摘要

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.

並列關鍵字

strong ； strict converse duality theorem ； weak ； parametric type dual ； Mond-Weir type dual ； Wolfe type dual

參考文獻

[1] T. Antczak, Multiobjective Programming under d-invexity, European Journal of

[2] T. Antczak, The Notion of V-r-Invexity in Differentiable Multiobjective Programming, J.

[3] D. Bhatia and S. Pandey, A Note on Multiobjective Fractional Programming, Cahiers du

Cero, 33 (1991), 3-11.

[5] N. Datta, Efficiency in Multi-Objective Fractional Programming, J. Inform. Optim. Sci.