On robustness for set-valued optimization problems

被引:0
作者
Kuntal Som
V. Vetrivel
机构
[1] Indian Institute of Technology Madras,Department of Mathematics
来源
Journal of Global Optimization | 2021年 / 79卷
关键词
Set-valued optimization; Robustness; Uncertainty;
D O I
暂无
中图分类号
学科分类号
摘要
In the recent past, finding robust solutions for optimization problems contaminated with uncertainties has been topical and has been investigated in the literature for scalar and multi-objective/vector-valued optimization problems. In this paper, we introduce various types of robustness concept for set-valued optimization, such as min–max set robustness, optimistic set robustness, highly set robustness, flimsily set robustness, multi-scenario set robustness. We study some existence results for corresponding concepts of solution and establish some relationship among them.
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页码:905 / 925
页数:20
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共 42 条
  • [1] Bitran GR(1980)Linear multiple objective problems with interval coefficients Manag. Sci. 26 694-706
  • [2] Ben-Tal A(1998)Robust convex optimization Math. Oper. Res. 23 769-805
  • [3] Nemirovski A(2009)Duality in robust optimization: primal worst equals dual best Oper. Res. Lett. 37 1-6
  • [4] Beck A(2019)Dominance for multi-objective robust optimization concepts Eur. J. Oper. Res. 273 430-440
  • [5] Ben-Tal A(2017)Quasiconvexity of set-valued maps assures well-posedness of robust vector optimization Ann. Oper. Res. 251 89-104
  • [6] Botte M(2014)Minmax robustness for multi-objective optimization problems Eur. J. Oper. Res. 239 17-31
  • [7] Schöbel A(2010)Duality for set-valued measures of risk SIAM J. Financ. Math. 1 66-95
  • [8] Crespi GP(2011)Set-valued risk measures for conical market models Math. Financ. Econ 5 1-28
  • [9] Kuroiwa D(2018)Cone distribution functions and quantiles for multivariate random variables J. Multivar. Anal. 167 97-113
  • [10] Rocca M(2018)A set optimization approach to zero-sum matrix games with multi-dimensional payoffs Math. Methods Oper. Res. 88 369-397