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向量D-η-E-半预不变凸映射与向量优化

彭再云 李科科 张石生

彭再云, 李科科, 张石生. 向量D-η-E-半预不变凸映射与向量优化[J]. 应用数学和力学, 2014, 35(9): 1020-1032. doi: 10.3879/j.issn.1000-0887.2014.09.008
引用本文: 彭再云, 李科科, 张石生. 向量D-η-E-半预不变凸映射与向量优化[J]. 应用数学和力学, 2014, 35(9): 1020-1032. doi: 10.3879/j.issn.1000-0887.2014.09.008
PENG Zai-yun, LI Ke-ke, ZHANG Shi-sheng. D-η-E-Semipreinvex Vector Mappings and Vector Optimization[J]. Applied Mathematics and Mechanics, 2014, 35(9): 1020-1032. doi: 10.3879/j.issn.1000-0887.2014.09.008
Citation: PENG Zai-yun, LI Ke-ke, ZHANG Shi-sheng. D-η-E-Semipreinvex Vector Mappings and Vector Optimization[J]. Applied Mathematics and Mechanics, 2014, 35(9): 1020-1032. doi: 10.3879/j.issn.1000-0887.2014.09.008

向量D-η-E-半预不变凸映射与向量优化

doi: 10.3879/j.issn.1000-0887.2014.09.008
基金项目: 国家自然科学基金(11301571; 11271389); 重庆市自然科学基金(CSTC2012jjA00016); 重庆市教委科技项目(KJ130428)
详细信息
    作者简介:

    彭再云(1980—),男,重庆人,副教授,博士(E-mail: pengzaiyun@126.com);张石生(1934—),男,云南曲靖人,教授(通讯作者. E-mail: changss@yahoo.cn).

  • 中图分类号: O221.1

D-η-E-Semipreinvex Vector Mappings and Vector Optimization

Funds: The National Natural Science Foundation of China(11301571; 11271389)
  • 摘要: 提出了一类新的向量值映射——D- η -E-半预不变凸映射, 它是E-预不变凸映射与D- η -半预不变凸映射的真推广.首先, 用例子说明了E-半不变凸集、D- η -E-半预不变凸映射的存在性;然后,给出了D- η -E-半预不变凸映射的判定定理, 并讨论了D- η -E-半预不变凸映射与D- η -E-严格/半严格半预不变凸映射的关系;最后,得到了D- η -E-半严格半预不变凸映射在隐约束优化问题中的一个重要应用,并举例验证了所得结果.
  • [1] Hanson M A. On sufficiency of the Kuhn-Tucker conditions[J].Journal of Mathematical Analysis and Applications,1981,80(2): 545-550.
    [2] Ben-Israel A, Mond B. What is invexity?[J].The Journal of the Australian Mathematical Society,1986,28(1): 1-9.
    [3] Weir T, Jeyakumar V. A class of nonconvex functions and mathematical programming[J].Bulletin of Australian Mathematical Society,1998,38(2): 177-189.
    [4] YANG Xin-min, LI Duan. On properties of preinvex functions[J].Journal of Mathematical Analysis and Applications,2001,256(1): 229-241.
    [5] YANG Xin-min, LI Duan. Semistrictly preinvex functions[J].Journal of Mathematical Analysis and Applications,2001,258(1): 287-308.
    [6] Yang 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.
    [7] Peng Z Y, Chang S S. Some properties of semi-G-preinvex functions[J].Taiwanese Journal of Mathematics, 2013,17(3): 873-884.
    [8] Antczak T.G-pre-invex functions in mathematical programming [J].Journal of Computational and Applied Mathematics,2008,217(1): 212-226.
    [9] Kazmi K R. Some remarks on vector optimization problems[J].Journal of Optimization Theory and Applications,1998,96(1): 133-138.
    [10] PENG Jian-wen, ZHU Dao-li. On D-preinvex type functions[J].Journal of Inequalities and Applications,2006,2006. Article ID 93532: 1-14 .
    [11] Long X J, Peng Z Y, Zeng B. Remark on cone semistrictly preinvex functions[J].Optimization Letters,2009,3(3): 337-345.
    [12] 彭建文.向量值映射D-η-预不变真拟凸的性质[J]. 系统科学与数学, 2003,23(3):306-314.(PENG Jian-wen. Properties of D-η-properly prequasinvex functions[J].Journal of Systems Science and Mathematical Sciences,2003,23(3):306-314.(in Chinese))
    [13] 彭建文. 广义凸性及其在最优化问题中的应用[D]. 博士学位论文. 呼和浩特: 内蒙古大学理工学院, 2005.(PENG Jian-wen. Generalized convexity with application optimization problems[D]. PhD Thesis. Hohhot:Inner Mongolia University,2005.(in Chinese))
    [14] Fulga C, Preda V. Nonlinear programming with E-preinvex and local E-preinvex functions [J].European Journal of Operational Research,2009,192(3): 737-743.
    [15] 彭再云, 王堃颍, 赵勇, 张石生. D-η-半预不变凸映射的性质及其应用[J]. 应用数学和力学, 2014,35(2): 202-211.(PENG Zai-yun, WANG Kun-ying, ZHAO Yong, ZHANG Shi-sheng. Characterizations and applications of D-η-semipreinvex mappings[J].Applied Mathematics and Mechanics,2014, 35(2): 202-211.(in Chinese))
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  • 被引次数: 0
出版历程
  • 收稿日期:  2014-04-05
  • 刊出日期:  2014-09-15

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