留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

可变序结构下向量优化中的一个新非线性标量化函数及其应用

李飞

李飞. 可变序结构下向量优化中的一个新非线性标量化函数及其应用[J]. 应用数学和力学, 2020, 41(3): 329-338. doi: 10.21656/1000-0887.400262
引用本文: 李飞. 可变序结构下向量优化中的一个新非线性标量化函数及其应用[J]. 应用数学和力学, 2020, 41(3): 329-338. doi: 10.21656/1000-0887.400262
LI Fei. A New Nonlinear Scalarization Function and Its Applications in Vector Optimization With Variable Ordering Structures[J]. Applied Mathematics and Mechanics, 2020, 41(3): 329-338. doi: 10.21656/1000-0887.400262
Citation: LI Fei. A New Nonlinear Scalarization Function and Its Applications in Vector Optimization With Variable Ordering Structures[J]. Applied Mathematics and Mechanics, 2020, 41(3): 329-338. doi: 10.21656/1000-0887.400262

可变序结构下向量优化中的一个新非线性标量化函数及其应用

doi: 10.21656/1000-0887.400262
基金项目: 国家自然科学基金(11431004;11601248)
详细信息
    作者简介:

    李飞(1981—),男,讲师,博士(E-mail: lifeimath@163.com).

  • 中图分类号: O221.6

A New Nonlinear Scalarization Function and Its Applications in Vector Optimization With Variable Ordering Structures

Funds: The National Natural Science Foundation of China(11431004;11601248)
  • 摘要: 在具有可变序结构的一般拓扑向量空间中定义了一个新的非线性标量化函数,讨论了该函数的主要性质.同时作为应用,通过该函数构造出了一族半范数和一类赋范线性空间,并在最后建立了该非线性标量化函数和半范数的上、下半连续性结论.
  • [1] YANG X M, YANG X Q, CHEN G Y. Theorems of the alternative and optimization with set-valued maps[J]. Journal of Optimization Theory and Applications,2000,107(3): 627-640.
    [2] YANG X M, LI D, WANG S Y. Near-subconvexlikeness in vector optimization with set-valued functions[J]. Journal of Optimization Theory and Applications,2001,110(2): 413-427.
    [3] 吴海琴, 刘学文, 罗萍. 集值优化问题广义近似解的线性标量化[J]. 重庆师范大学学报(自然科学版), 2017,34(4): 13-16.(WU Haiqin, LIU Xuewen, LUO Ping. Nonlinear scalarization theorems of generalized approximate solutions in set-valued optimization problems[J]. Journal of Chongqing Normal University(Natural Science),2017,34(4): 13-16.(in Chinese))
    [4] 刘学文, 王婷, 汪定国. 向量优化中广义 E -Benson真有效解的性质研究[J]. 重庆师范大学学报(自然科学版), 2018,35(3): 17-20.(LIU Xuewen, WANG Ting, WANG Dingguo. Characterizations of generalized E -Benson proper efficient solutions in vector optimization[J]. Journal of Chongqing Normal University(Natural Science),2018,35(3): 17-20.(in Chinese))
    [5] GERSTEWITZ C H, IWANOW E. Dualitt für nichtkonvexe vektoroptimierungsprobleme[J]. Wissensch Zeitschr Tech,1985,31: 61-81.
    [6] LUC D T. Theory of Vector Optimization [M]. Berlin: Springer, 1989.
    [7] GERTH C, WEIDNER P. Nonconvex separation theorems and some applications in vector optimization[J]. Journal of Optimization Theory and Applications,1990,67(2): 297-320.
    [8] GPFERT A, RIAHI H, TAMMER C, et al. Variational Methods in Partially Ordered Spaces [M]. New York: Springer, 2003.
    [9] CHEN G Y, HUANG X X, YANG X Q. Vector Optimization-Set-Valued and Variational Analysis [M]. Berlin: Springer, 2005.
    [10] JAHN J. Vector Optimization-Theory, Applications and Extensions [M]. 2nd ed. Berlin: Springer, 2011.
    [11] 戎卫东, 杨新民. 向量优化及其若干进展[J]. 运筹学学报, 2014,18(1): 9-38.(RONG Weidong, YANG Xinmin. Vector optimization and its developments[J]. Operations Research Transactions,2014,18(1): 9-38.(in Chinese))
    [12] 李伟佳, 朱巧, 赵克全. Gerstewitz非线性标量化函数的性质及其在向量优化中的应用[J]. 重庆师范大学学报(自然科学版), 2017,34(5): 1-5.(LI Weijia, ZHU Qiao, ZHAO Kequan. Properties of Gerstewitz nonlinear scalarization function and applications in vector optimization[J]. Journal of Chongqing Normal University(Natural Science),2017,34(5): 1-5.(in Chinese))
    [13] 朱巧, 徐威娜, 赵克全. 向量优化中Gerstewitz非线性标量化函数的拟内部性质[J]. 重庆师范大学学报(自然科学版), 2018,35(1): 11-14.(ZHU Qiao, XU Weina, ZHAO Kequan. Properties of Gerstewitz nonlinear scalarization function via quasi interiors in vector optimization[J]. Journal of Chongqing Normal University(Natural Science),2018,35(1): 11-14.(in Chinese))
    [14] ZHAO K Q, ZHU Q, WANG D G. Nonconvex separation theorems via assumption B and applications in vector optimization[J]. Journal of Chongqing Normal University(Natural Science),2018,〖STHZ〗 35(3): 1-8.
    [15] YU P L. Multiple-Criteria Decision Making: Concepts, Techniques and Extensions [M]. New York: Plenum Press, 1985.
    [16] EICHFELDER G. Variable Ordering Structures in Vector Optimization [M]. Berlin: Springer, 2014.
    [17] CHEN G Y, YANG X Q. Characterizations of variable domination structures via nonlinear scalarization[J]. Journal of Optimization Theory and Applications,2002,112(1): 97-110.
    [18] CHEN G Y, YANG X Q, YU H. A nonlinear scalarization function and generalized quasi-vector equilibrium problems[J]. Journal of Global Optimization,2005,32(4): 451-466.
    [19] FARAJZADEH A, LEE B S, PLUBTEING S. On generalized quasi-vector equilibrium problems via scalarization method[J]. Journal of Optimization Theory and Applications,2015,168(2): 1-16.
    [20] 邵重阳, 彭再云, 王泾晶, 等. 参数广义弱向量拟平衡问题解映射的H-连续性刻画[J]. 应用数学和力学, 2019,40(4): 452-462.(SHAO Chongyang, PENG Zaiyun, WANG Jingjing, et al. Characterizations of H-continuity for solution mapping to parametric generalized weak vector quasi-equilibrium problems[J]. Applied Mathematics and Mechanics,2019,40(4): 452-462.(in Chinese))
    [21] LUC D T, RA ?瘙 塃 IU A. Vector optimization: basic concepts and solution methods[M]//AL-MEZEL S A R, AL-SOLAMY F R M, ANSARI Q H, ed.Fixed Point Theory, Variational Analysis and Optimization . Boca Raton: CRC Press, Taylor & Francis Group, 2014.
  • 加载中
计量
  • 文章访问数:  619
  • HTML全文浏览量:  108
  • PDF下载量:  337
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-09-04
  • 修回日期:  2019-09-24
  • 刊出日期:  2020-03-01

目录

    /

    返回文章
    返回