廣義凸函數的探討

On Generalized Convex Functions

黃建達(Jian-Da Huang)

指導教授 ： 蕭育如 博士

元智大學/工程學院/工業工程與管理學系/碩士(2000年)

摘要

在本論文中，透過減弱凸函數與擬凸函數的定義，我們提出了弱凸函數與弱擬凸函數的概念。我們並建立了定義在 的閉凸子集上的下半連續函數為凸函數或擬凸函數之充分必要條件。另外，我們也定義 $-convex函數和 $-B-vex凸函數，同時也提出這兩類廣義凸函數的特徵定理與一些相關性質。

關鍵字

凸性 ； 弱凸性 ； 半連續性

並列摘要

A class of functions called weakly convex and weakly quasiconvex functions is introduced by relaxing the definitions of convex and quasiconvex functions. Necessary and sufficient conditions, under which a lower semi-continuous function on a nonempty closed convex subsets of the n-dimensional Euclidean space is convex or quasiconvex are established. Another class of functions, called $-convex and $-B-vex, is defined. Some properties for these functions are presented.

並列關鍵字

convexity ； quasiconvexity ； weak convexity ； lower semi-continuity

參考文獻

[6] Pini, P., and C. Singh, 〝 ($1,$2)-Convexity,〞 Optimization, Vol. 40, pp. 103-120, 1997.

[14] Suneja, S. K., C. Singh, and C. R. Bector, Generalization of Preinvex and B-vex Functions,〞 Journal of Optimization Theory and Applications, Vol. 76, No. 3, p.p. 577-587, March 1993.

[1] Yang, X. M., 〝Convexity of Semi-Continuous Functions,〞 Opsearch,Vol.31, No. 4, pp. 309-317, 1994.

[5] Weir, T., and B. Mond., 〝Preinvex functions in multiple Objective Optimization,〞 Journal of Mathematical Analysis and Applications, Vol. 136, pp. 29-38, 1988.

References