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关于预不变拟凸函数的一些特征(英文) 被引量：3

On Characterizations of Prequasiinvex Functions
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摘要 给出了预不变拟凸函数的必要条件,并利用该必要条件证明了严格预不变拟凸函数的等价条件,最后给出了中间点预不变拟凸函数的充分必要条件. Some characterizations about prequasiinvex functions are obtained.Firstly,a necessary condition about prequasiinvex functions is established.Secondly,a necessary and sufficient condition of strictly prequasiinvex functions is provided by making use of the necessary condition.Finally,a necessary and sufficient condition is established about intermediate-point prequasiinvex functions.
作者 赵克全 刘学文 陈哲
机构地区 重庆师范大学数学与计算机科学学院
出处 《西南大学学报（自然科学版）》 CAS CSCD 北大核心 2010年第7期30-33,共4页 Journal of Southwest University(Natural Science Edition)
基金 国家自然科学基金资助项目(10771228) 重庆师范大学青年基金资助项目(08XLQ01)
关键词 不变凸集 预不变拟凸函数 严格预不变拟凸函数 中间点预不变拟凸函数 invex set prequasiinvex function strictly prequasiinvex function intermediate point prequasiinvex function
分类号 O221.2 [理学—运筹学与控制论]
  • 相关文献

参考文献10

  • 1Weir T, Mond B. Preinvex Functions in Multi-objective Optimization [J]. Journal of Mathematical Analysis and Applications, 1988, 136: 29-38.
  • 2Weir T, Jeyakumar V. A Class of Nonconvex Functions and Mathematical Programming [J]. Bulletin of Australian Mathematical Society, 1988, 38:177 - 189.
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  • 5Yang X M, Yang X Q, Teo K L. Characterizations and Applications of Prequasi-invex Functions [J]. Journal of Optimization Theory and Applications, 2001, 110: 645 -668.
  • 6Yang X M, Li D. On Properties of Preinvex Function [J]. Journal of Mathematical Analysis and Applications, 2001, 256: 229-241.
  • 7Yang X M, Li D. Semistrictly Preinvex Functions [J]. Journal of Mathematical Analysis and Applications, 2001, 258: 287 - 308.
  • 8Hadjisawas N, Schaible S. On Strong Pseudomonotonicity and (Semi) Strict Quasimonotonicity [J]. Journal of Optimization Theory and Applications, 1993, 79: 139- 155.
  • 9旷华武,颜宝平.用近似凸性研究拟凸函数[J].西南师范大学学报（自然科学版）,2004,29(1):25-28. 被引量：7
  • 10杨勇.B_ε-不变凸分式半无限规划的ε-最优性[J].西南大学学报（自然科学版）,2009,31(9):58-60. 被引量：4

二级参考文献5

  • 1Jeyakumar V, Mond B. On Generalized Convex Mathematical Programming [J]. J Austral Math Soc Ser B, 1992. 34(1): 43-53. 2007.
  • 2Hanson M A. On Sufficiency of the Kuhn-Tucker Condition [J]. J Math Anal Appl, 1981, 80:545-550.
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共引文献9

同被引文献17

  • 1WEIR T, MOND B. Prieinvex Functions in Multiple Objective Optimization [J]. Journal of Math Anal and Appl, 1988, 136:29 38.
  • 2WEIR T, JEYAKWMAR V. A Class of Nonconvex Functions and Mathematical Programming [J]. Bulletin of Austral ian Mathematical Society, 1988, 38(2): 177 189.
  • 3YANG X M, LID. Semistrictly Preinvex Functions [J]. Journal of Mathematical Analysis and Applications, 2001, 258.- 287-308.
  • 4NOOR M A, NOOR K I. Some Characterizations of Strongly Preinvex Functions [J]. Journal of Mathematical Analysis and Applications, 2006, 316(2): 697-706.
  • 5ROBERTS A W, VARBERG D E. Convex Functions [M]. New York: Acdemic Press, 1973.
  • 6YANG X M, LI D. On Properties of Preinvex Functions [J]. Journal of Mathematical Analysis and Applications, 2001, 256(1) : 229-241.
  • 7AVRIEL M, DIEWERT W E, SCHAIBLE S S, et al. Generalized Concavity [M]. New York: Penum Press, 1988.
  • 8YANG X M. Semistrictly Convex Functions [J]. Opsearch, BAZARAA M S, SHETTY C M. Nonlinear Programming Sons, 1979. 1994, 31(1): 15-27.
  • 9Theory and Algorithms EM. New York: John Wiley and NOOR M A. On Generalized Preinvex Functions and Monotonicities [J]. Journal of Inequality Pure Applied Mathemat ics, 2004, 5(4): 1-9.
  • 10LIU C P. Some Characterizations and Applications on Strongly a-preinvex and Strongly a-Invex Functions [J]. Journal of Industrial and Management Optimization, 2008, 4(4) : 727- 738.

引证文献3

二级引证文献14

西南大学学报（自然科学版）
2010年 第7期

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