• • 上一篇    下一篇

一类集值优化最小解的存在性与适定性及应用

卢婧琦, 洪世煌, 江俊   

  1. 杭州电子科技大学理学院 杭州 310018
  • 收稿日期:2021-05-06 修回日期:2021-10-08 出版日期:2022-04-25 发布日期:2022-06-18
  • 通讯作者: 洪世煌,Email:hongshh@hotmail.com.
  • 基金资助:
    国家自然科学基金(71771068,71471051)资助课题.

卢婧琦, 洪世煌, 江俊. 一类集值优化最小解的存在性与适定性及应用[J]. 系统科学与数学, 2022, 42(4): 1011-1022.

LU Jingqi, HONG Shihuang, JIANG Jun. The Existence and Well-Posedness of Minimum Solutions for a Class of Set-Valued Optimization Problems with Applications[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(4): 1011-1022.

The Existence and Well-Posedness of Minimum Solutions for a Class of Set-Valued Optimization Problems with Applications

LU Jingqi, HONG Shihuang, JIANG Jun   

  1. College of Science, Hangzhou Dianzi University, Hangzhou 310018
  • Received:2021-05-06 Revised:2021-10-08 Online:2022-04-25 Published:2022-06-18
This paper deals with the existence and $l$-${ B}_Z$-well-posedness of the minimum solutions for a class of set-valued optimization problems by using the set valued analysis theory. First, in view of the introduced $\overline{\mathbb{R}}_+$-local-inclusion property and $\mathbb{R}_-$-weakly transfer lower semicontinuity in a vector space, a new definition of the $C({\rm int}C)$-local inclusion and lower semi-continuity with the $C^Z\big(({\rm int}C)^Z\big)$-weak transfer is given. Next, the sufficient conditions for the existence of minimum solutions for set-valued optimizations are presented by using the character mentioned above. Finally, as an application of the obtained results, a class of vector valued games with uncertainty is discussed and present sufficient conditions for the existence of a robust Nash equilibria with the $l$-${ B}_Z$-well-posedness are presented.

MR(2010)主题分类: 

()
[1] Kuroiwa D. Some criteria in set-valued optimization. Suurikaisekikenkyusho Kookyuroku, 1997, 985:171-176.
[2] Kuroiwa D. On set-valued optimization. Nonlinear Anal. TMA, 2001, 47(2):1395-1400.
[3] Kuroiwa D. Existence theorems of set optimization with set-valued maps. J. Inform. Optim. Sci., 2003, 24(1):73-84.[1] Kuroiwa D. Some criteria in set-valued optimization. Suurikaisekikenkyusho Kookyuroku, 1997, 985:171-176.
[2] Kuroiwa D. On set-valued optimization. Nonlinear Anal. TMA, 2001, 47(2):1395-1400.
[3] Kuroiwa D. Existence theorems of set optimization with set-valued maps. J. Inform. Optim. Sci., 2003, 24(1):73-84. 1022 P=1 n#n 42+
[4] Alonso M, Rodr′ıguez-Mar′ın L. Set-relations and optimality conditions in set-valued maps. Nonlinear Anal., 2005, 63(8):1167-1179.
[5] Hernández E, Rodr′ıguez-Mar′ın L. Existence theorems for set optimization problems. Nonlinear Anal., 2006, 67(6):1726-1736.
[6] Gupta M, Srivastava M. Well-posedness and scalarization in set optimization involving ordering cones with possibly empty interior. J. Glob. Optim., 2019, 73(2):447-463.
[7] Gutiérrez C, Miglierina E, Molho E, et al. Pointwise well-posedness in set optimization with cone proper sets. Nonlinear Anal. TMA, 2012, 75:1822-1833.
[8] Han Y, Huang N J. Well-posedness and stability of solutions for set optimization problems. Optim., 2017, 66(1):17-33.
[9] Khoshkhabar-amiranloo S. Characterizations of generalized Levitin-Polyak well-posed set optimization problems. Optim. Lett., 2019, 13:147-161.
[10] Long X J, Peng J W. Generalized B-well-posedness for set optimization problems. J. Optim. Theory Appl., 2013, 157(3):612-623.
[11] Long X J, Peng J W, Peng Z Y. Scalarization and pointwise well-posedness for set optimization problems. J. Glob. Optim., 2015, 62(4):763-773.
[12] Vui P T, Anh L Q, Wangkeeree R. Levitin-Polyak well-posedness for set optimization problems involving set order relations. Positivity, 2019, 23(3):599-616.
[13] Zhang W Y, Li S J, Teo K L. Well-posedness for set optimization problems. Nonlinear Anal. TMA, 2009, 71(9):3769-3778.
[14] Crespi G P, Dhingra M, Lalitha C S. Pointwise and global well-posedness in set optimization:Adirect approach. Ann. Oper. Res., 2018, 269(1):149-166.
[15] Zhang C L, Huang N J. On the stability of minimal solutions for parametric set optimization problems. Appl. Anal., 2021, 100(7):1533-1543.
[16] Zhang C L, Huang N J. Well-posedness and stability in set optimization with applications. Positivity, 2021, 25(3):1153-1173.
[17] Geoffroy M H. A topological convergence on power sets well-suited for set optimization. J. Glob. Optim., 2019, 73(3):567-581.
[18] Eslamizadeh L, Naraghirad E. Existence of solutions of set-valued equilibrium problems in topological vector spaces with applications. Optim. Lett., 2020, 14(1):65-83.
[19] Goubault-Larrecq J. Non-Hausdorff Topology and Domain Theory. Cambridge:Cambridge University Press, 2013.
[20] Rubin W. Principles of Mathematical Analysis. New York:McGraw-Hill, 1976.
[21] Hernández E, Rodr′ıguez-Mar′ın L. Nonconvex sclaraization in set optimization with set-valued maps. J. Math. Anal. Appl., 2007, 325:1-18.
[22] Jahn J, Ha T X D. New order relations in set optimization. J. Optim. Theory Appl., 2011, 148(2):209-236.
[1] 侯震梅;周勇. 扰动集值优化问题超有效点集的次微分稳定性[J]. 系统科学与数学, 2006, 26(6): 744-751.
[2] 徐义红;刘三阳. 近似锥-次类凸集值优化的严有效性[J]. 系统科学与数学, 2004, 24(3): 311-317.
阅读次数
全文


摘要