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向量值D-半预不变真拟凸映射的判定与性质 被引量：4

Characterizations and Criterions of D-Semiprequasi-invex Mappings
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摘要 提出了一类新的向量值映射—D-半预不变真拟凸映射,它是D-预不变真拟凸映射与D-半预不变凸映射的真推广。首先,给出例子说明半不变凸集、D-半预不变真拟凸映射的存在性;然后,给出了相关集合的稠密性结果以及在下D-半连续条件下D-半预不变真拟凸映射的判定,并建立了D-半预不变真拟凸映射与D-严格/半严格半预不变真拟凸映射间的关系;最后,讨论了D-半严格半预不变真拟凸映射在向量优化问题中的一个应用,并举例验证了所得结论的正确性。 A class of new vector valued generalized convex mappings--D-semiprequsai-invex mappings, which is a true generalization of D-prequasi-invex mapping[14] and D-semipre-invex mapping[15], is given in this paper. Firstly, examples are given to show the existence of semi-invex sets and D-semiprequasi-invex mappings. Secondly, the density result of corresponding set and a criterion of D-semiprequasi-invexity under the condition of D-lower semicontinuous are given. Then, the relationships among D-semiprequasi- invexity, D-strictly semiprequasi-invexity and D-semistrictly semiprequasi-invexity are discussed; Finally, an important application of D-semiprequasi-invexity in vector optimization problem is obtained, and some examples are given to illustrate the results.
作者 彭再云 李科科 唐平 黄应全
机构地区 重庆交通大学理学院 重庆师范大学数学学院 重庆文理学院数学与财经学院 重庆工商大学数学与统计学院
出处 《重庆师范大学学报（自然科学版）》 CAS CSCD 北大核心 2014年第5期18-25,共8页 Journal of Chongqing Normal University:Natural Science
基金 国家自然科学基金(No.11271389) 国家青年基金(No.11301571) 重庆市自然科学基金(No.2012jjA00016) 重庆市教委基金项目(No.KJ130428) 重庆交通大学创新训练项目(2014年)
关键词 半不变凸集 D-半预不变真拟凸映射 判定定理 向量优化 应用 semi-invex sets D- semi-prequasi-invex mappings criterion vector optimization applications
分类号 O221 [理学—运筹学与控制论]
  • 相关文献

参考文献14

  • 1Hanson M A. On sufficiency of the Kuhn-Tucker condi tions[J]. Journal of Mathematical Analysis and Applica- tions, 1981,80 (2) : 545-550.
  • 2Ben-Israel A,Mond B. What is invexity?[J]. Journal of the Australian Mathematical Society, 1986,28 : 1-9.
  • 3Weir T,Jeyakumar V. A class of nonconvex functions and mathematical programming [J].Bulletin of Australian Mathematical Society, 1998,38 : 177-189.
  • 4Yang X M, Li D. On properties of preinvex functions[J]. Journal of Mathematical Analysis and Applications, 2001, 256(1) :229-241.
  • 5Yang X M, Li D. Semistrictly preinvex functions[J]. Jour- nal of Mathematical Analysis and Applications, 2001,258 (1) : 287-308.
  • 6Yang X Q,Chen G. A class of nonconvex functions and pre- variational inequalities[J]. Journal of Mathematical Analy- sis and Applications, 1992,169 (2) : 359-373.
  • 7Peng Z Y,Chang S S. Some properties of semi-G-preinvex- functions[J]. Taiwan Residents Journal of Mathematics, 2013,17 (3) :873-884.
  • 8Antczak T. G-pre-invex functions in mathematical pro- gramming[J]. Journal of Computational and Applied Math- ematics, 2008,217: 212-226.
  • 9Kazmi K R. Some remarks on vector optimization problems[J]. Journal of Optimization Theory and Applications, 1998,96(1) :133-138.
  • 10Peng J W, Zhu D L. On D-preinvex type functions[J]. Journal of Inequalities and Applications, 2006, Article ID 93532:1-14.

二级参考文献14

  • 1Hanson M A. On sufficiency of the Kuhn-Tucker conditions[J].Journal of Mathematical A?nalysis and Applications, 1981, 80( 2) : 545-550.
  • 2Ben- Israel A, Mond B. What is invexity?[J].Journal of the Australian Mathematical Socie?ty, 1986,28: 1-9.
  • 3Weir T,Jeyakumar V. A class of nonconvex functions and mathematical programming[J] . Bulletin of Australian Mathematical Society, 1988,38: 177-189.
  • 4Yang X M, Li D. On properties of preinvex functions[J].Journal of Mathematical Analysis and Applications, 2001, 256( 1) : 229-241.
  • 5Yang X M, Li D. Semistrictly preinvex functionsJ J].Journal of Mathematical Analysis and Applications, 2001, 258( 1) : 287-308.
  • 6Yang X Q, Chen G Y. A class of nonconvex functions and pre-variational inequalities[J]. Journal of Mathematical Analysis and Applications, 1992, 169(2) : 359-373.
  • 7Peng Z Y, Chang S S. Some properties of semi-G-preinvex functions[J]. TaiwaneseJournal of Mathematics, 2013, 17( 3) : 873-884.
  • 8Antczak T. G-pre-invex functions in mathematical progranuning[J].Journal of Computation?al and Applied Mathematics, 2008, 217( 1) : 212-226.
  • 9Kazmi K R. Some remarks on vector optimization problems[J] .Journal of Optimization The?ory and Applications, 1998, 96( 1): 133-138.
  • 10PengJ W, Zhu D L. On D-preinvex-type functionsJ J}.Journal of Inequalities and Applica?tions, 2006, 2006: 093532. doi , 10.1155/JW2006/93532.

共引文献17

同被引文献18

  • 1龙宪军,毛小红.关于向量值映射D-η预不变真拟凸的注记[J].云南民族大学学报（自然科学版）,2005,14(3):213-215. 被引量：1
  • 2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
  • 3Luo Hezhi,Wu Huixian,Zhu Yihua.NEW METHODS FOR CHARACTERIZING D-η-PROPERLY PREQUASI-INVEX FUNCTIONS[J].Applied Mathematics(A Journal of Chinese Universities),2006,21(1):107-112. 被引量：4
  • 4Hanson M A.On sufficiency of the Kuhn-Tucker conditions[J].Journal of Mathematical Analysis and Applications,1981,80(2): 545-550.
  • 5Weir T,Mond B.Pre-invex functions in multiple objective optimization[J].Journal of Mathematical Analysis and Applications,1988,136(1): 29-38.
  • 6Weir T,Jeyakumar V.A class of nonconvex functions and mathematical programming[J].Bulletin of the Australian Mathematical Society,1988,38(2): 177-189.
  • 7Mohan S R,Neogy S K.On invex sets and preinvex functions[J].Journal of Mathematical Analysis and Applications,1995,189(3): 901-908.
  • 8Yang X M,Li D.On properties of preinvex functions[J].Journal of Mathematical Analysis and Applications,2001,256(1): 229-241.
  • 9Yang X M,Li D.Semistrictly preinvex functions[J].Journal of Mathematical Analysis and Applications,2001,258(1): 287-308.
  • 10Yang J,Yang X.Two new characterizations of preinvex functions[J].Dynamics of Continuous,Discrete & Impulsive Systems B,2012,19(3): 405-410.

引证文献4

二级引证文献10

重庆师范大学学报（自然科学版）
2014年 第5期

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