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预不变凸性判别准则的新证明 被引量：2

A New Proof of Criteria for Preinvexity
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摘要 在适当条件下,函数的预不变凸性可利用函数的中间点预不变凸性进行判断.文章利用上半连续函数在紧集上必存在最大值的性质提出了预不变凸性判别准则的新的证明方法.该证明方法简化了已有的证明方法,且无需集合开性的假设. Preinvexity of functions can be verified in terms of intermediate-point preinvexity of functions under some suitable conditions.In this paper,a new method to prove criteria for preinvexity is given in terms of the result that there must exist a maximum for any upper semicontinuous function defined on a compact set.This method simplifies the primal proof and the set is not necessarily an open set.
作者 赵克全 郭辉
机构地区 重庆师范大学数学学院
出处 《西南大学学报（自然科学版）》 CAS CSCD 北大核心 2012年第8期119-121,共3页 Journal of Southwest University(Natural Science Edition)
基金 国家自然科学基金资助项目(11126348 11171363) 重庆市运筹学与系统工程市级重点实验室专项基金资助项目(CSTC 2011KLORSE02) 重庆市教委科技项目(KJ110625)
关键词 不变凸集 预不变凸性 上半连续 invex set preinvexity upper semicontinuity
分类号 O224 [理学—运筹学与控制论]
  • 相关文献

参考文献7

  • 1WEIR T, MOND B. Preinvex Functions in Multi-Objective Optimization [J]. Journal of Mathematical Analysis and Ap plications, 1988, 136(1): 29-38.
  • 2WEIR T, JEYAKUMAR V. A Class of Nonconvex Functions and Mathematical Programming [J]. Bulletin of the Aus tralian Mathematical Society, 1988, 38(2): 177-189.
  • 3MOHAN S R, NEOGY S K. On Invex Sets and Preinvex Functions [J].Journal of Mathematical Analysis and Applica tions, 1995, 189(3): 901-908.
  • 4YANG Xin-ming, LI Duan. On Properties of Preinvex Function [J]. Journal of Mathematical Analysis and Applications 2001, 256(1):229-241.
  • 5赵克全,陈哲,刘学文.关于G-预不变凸函数的一些性质[J].西南大学学报（自然科学版）,2011,33(3):14-17. 被引量：2
  • 6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
  • 7周志昂.广义凸集值向量优化问题的弱有效解[J].西南师范大学学报（自然科学版）,2005,30(2):221-225. 被引量：2

二级参考文献14

  • 1SCHAIBLE S, ZIEMBA W T. Generalized Concavity in Optimization and Economics [M]. London: Academic Press, 1981.
  • 2WEIR T, MOND B. Preinvex Functions in Multi-objective Optimization [J].Journal of Mathematical Analysis and Applications, 1988, 136.. 29-38.
  • 3WEIR T, JEYAKUMAR V. A Class of Nonconvex Functions and Mathematical Programming [J]. Bulletin of Australian Mathematical Society, 1988, 38: 177-189.
  • 4ANTCZAK T. G-preinvex Functions in Mathematical Programming [J]. Journal of Computational and Applied Mathematics, 2008, 217(1): 1-15.
  • 5MOHAN S R, NEOGY S K. On Invex Sets and Preinvex Functions [J]. Journal of mathematical Analysis and Applications, 1995, 189(3)I 901-908.
  • 6YANG X M, YANG X Q, TEO K L. Characterizations and Applications of Prequasiinvex Functions [J]. Journal of Optimization Theory and Applications, 2001, 110(3).. 645-668.
  • 7Li Z M. A Theorem of the Alternative and Its Applications to the Optimization of Set-Valued Maps [J]. Journal of Optimization Theory and Applications, 1999, 100(2) : 365 - 375.
  • 8Huang Y W. A Farkas-Minkowski Type Alternative Theorem and Its Applications to Set-Valued Equilibrium Problems [J]. Journal of Nonlinear and Convex Analysis, 2002, 3(1): 17 - 24.
  • 9Frenk J B G, Kassay G. On Classes of Generalized Convex Functions, Gordan-Farkas Type Theorem, and Lagrangian Duality [J]. Journal of Optimization Theory and Applications, 1999, 102(2):315 - 343.
  • 10Illes T, Kassay G. Theorems of the Alternative and Optimality Conditions for Convexlike and Convexlike Programming [J]. Journal of Optimization Theory and Applications, 1999, 101(2): 243 - 257.

共引文献8

同被引文献17

  • 1杨新民.半予不变凸性与多目标规划问题[J].重庆师范学院学报（自然科学版）,1994,11(1):1-5. 被引量：6
  • 2WEIR T, MOND B. Prieinvex Functions in Multiple Objective Optimization [J]. Journal of Math Anal and Appl, 1988, 136:29 38.
  • 3WEIR T, JEYAKWMAR V. A Class of Nonconvex Functions and Mathematical Programming [J]. Bulletin of Austral ian Mathematical Society, 1988, 38(2): 177 189.
  • 4YANG X M, LID. Semistrictly Preinvex Functions [J]. Journal of Mathematical Analysis and Applications, 2001, 258.- 287-308.
  • 5NOOR M A, NOOR K I. Some Characterizations of Strongly Preinvex Functions [J]. Journal of Mathematical Analysis and Applications, 2006, 316(2): 697-706.
  • 6ROBERTS A W, VARBERG D E. Convex Functions [M]. New York: Acdemic Press, 1973.
  • 7YANG X M, LI D. On Properties of Preinvex Functions [J]. Journal of Mathematical Analysis and Applications, 2001, 256(1) : 229-241.
  • 8AVRIEL M, DIEWERT W E, SCHAIBLE S S, et al. Generalized Concavity [M]. New York: Penum Press, 1988.
  • 9YANG X M. Semistrictly Convex Functions [J]. Opsearch, BAZARAA M S, SHETTY C M. Nonlinear Programming Sons, 1979. 1994, 31(1): 15-27.
  • 10Theory 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.

引证文献2

二级引证文献11

西南大学学报（自然科学版）
2012年 第8期

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