多目标优化问题鲁棒有效解与真有效解之间的关系

杨铭; 李林廷; 高英

doi:10.21656/1000-0887.400032

多目标优化问题鲁棒有效解与真有效解之间的关系

doi: 10.21656/1000-0887.400032

重庆师范大学数学科学学院, 重庆 401331

基金项目: 国家自然科学基金（11771064）

详细信息

作者简介:
杨铭（1995—），女，硕士生(E-mail: yming72@163.com);高英（1982—），女，教授，博士，硕士生导师(通讯作者. E-mail: gaoyingimu@163.com).

中图分类号: O221
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- 文章访问数: 1091
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- PDF下载量: 273
- 被引次数: 0
出版历程
- 收稿日期: 2019-01-14
- 修回日期: 2019-11-05
- 刊出日期: 2019-12-01

Relations Between Robust Efficient Solutions and Properly Efficient Solutions to Multiobjective Optimization Problems

School of Mathematical Sciences, Chongqing Normal University,Chongqing 401331, P.R.China

Funds: The National Natural Science Foundation of China（11771064）

摘要

摘要: 在一定条件下研究了多目标优化问题鲁棒有效解与真有效解之间的关系及鲁棒有效解的最优性条件.首先,给出多目标优化问题鲁棒弱有效解的概念,研究它与鲁棒有效解和真有效解之间的关系,举例说明了相关结果的合理性.其次,在次类凸和伪凸性假设下研究了鲁棒有效解的必要性条件和充分性条件.
- 多目标优化问题 /
- 鲁棒有效解 /
- 真有效解 /
- 最优性条件
Abstract: The relations between the robust efficient solutions and properly efficient solutions to multiobjective optimization problems were studied, and the optimality conditions for the robust efficient solutions were discussed. Firstly, the concept of weakly robust efficient solutions to multiobjective optimization problems was given. Then, the relations between the (weakly) robust efficient solutions and the properly efficient solutions were made clear. Several examples were given to illustrate the main results. Finally, the necessary and sufficient optimality conditions for the robust efficient solutions were established under the subconvexity and pseudoconvexity assumptions.
- multiobjective optimization problem /
- robust efficient solution /
- properly efficient solution /
- optimality condition

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参考文献(19)

[1]	KOOPMANS T C. Analysis of production as an efficient combination of activities[J]. Analysis of Production and Allocation,1951,158(1): 33-97.
[2]	KUHN H W, TUCKER A W. Nonlinear programming[C]// Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability.Berkeley, San Francisco, USA, 1951.
[3]	GEOFFRION A M. Proper efficiency and the theory of vector maximization[J]. Journal of Mathematical Analysis and Applications,1968,22(3): 618-630.
[4]	BORWEIN J M. Proper efficient points for maximizations with respect to cones[J]. SIAM Journal on Control and Optimization,1977,15(1): 57-63.
[5]	BENSON H P. An improved definition of proper efficiency for vector maximization with respect to cones[J]. Journal of Mathematical Analysis and Applications,1979,71(1): 232-241.
[6]	HENIG I. Proper efficiency with respect to cones[J]. Journal of Optimization Theory and Applications,1982,36(3): 387-407.
[7]	BENTAL A, NEMIROVSKI A. Robust truss topology design via semidefinite programming[J]. SIAM Journal on Optimization,1997,7(4): 991-1016.
[8]	KUROIWA D, LEE G M. On robust multiobjective optimization[J]. Journal of Nonlinear and Convex Analysis,2012,40(2/3): 305-317.
[9]	EHROGOTT M, IDE J, SCHOBEL A. Minimax robustness for multi-objective optimization problems[J]. European Journal of Operational Research,2014,239(1): 17-31.
[10]	IDE J, SCHOBEL A. Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts[J]. OR Spectrum,2016,38(1): 235-271.
[11]	GOBERNA M A, JEYAKUMAR V, LI G, et al. Robust solutions of multi-objective linear semi-infinite programs under constraint date uncertain[J]. SIAM Journal on Optimization,2014,24(3): 1402-1419.
[12]	GEORGIEV P J, LUC D T, PRDALOS P. Robust aspects of solutions in deterministic multiple objective linear programming[J]. European Journal of Operational Research,2013,229(1): 29-36.
[13]	ZAMANI M, SOLEIMANI-DAMANEH M, KABGANI A. Robustness in nonsmooth nonlinear multi-objective programming[J].European Journal of Operational Research,2015,247(2): 370-378.
[14]	MORTEZA R, MAJID S D. Robustness in deterministic vector optimization[J]. Journal of Optimization Theory and Applications,2018,179(1): 137-162.
[15]	SAWARAGI Y, NAKAYAMA H, TANINO T. Theory of Multiobjective Optimization [M]. London: Academic Press, 1985.
[16]	MARKO M M, PEKKA N. Nonsmooth Optimization [M]. London: World Scientific, 1992.
[17]	杨新民. Benson真有效解与Borwein真有效解的等价性[J]. 应用数学, 1994,7(2): 246-247.(YANG Xinmin. Equivalence between Benson proper efficient solution and Borwein proper efficient solution[J]. Applied Mathematics,1994,7(2): 246-247.(in Chinese))
[18]	李小燕, 高英. 多目标优化问题Proximal真有效解的最优性条件[J]. 应用数学和力学, 2015,36(6): 668-676.(LI Xiaoyan, GAO Ying. The optimality conditions of Proximal proper efficient solution for multi-objective optimization[J]. Applied Mathematics and Mechanics,2015,36(6): 668-676.(in Chinese))
[19]	FAKHAR M, MAHYARINIA M R, ZAFARANI J. On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization[J]. European Journal of Operational Research,2018,265(1): 39-48.

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多目标优化问题鲁棒有效解与真有效解之间的关系

doi: 10.21656/1000-0887.400032

作者简介:
杨铭（1995—），女，硕士生(E-mail: yming72@163.com);高英（1982—），女，教授，博士，硕士生导师(通讯作者. E-mail: gaoyingimu@163.com).

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Relations Between Robust Efficient Solutions and Properly Efficient Solutions to Multiobjective Optimization Problems

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留言板

多目标优化问题鲁棒有效解与真有效解之间的关系

doi: 10.21656/1000-0887.400032

作者简介: 杨铭（1995—），女，硕士生(E-mail: yming72@163.com);高英（1982—），女，教授，博士，硕士生导师(通讯作者. E-mail: gaoyingimu@163.com).

计量

出版历程

Relations Between Robust Efficient Solutions and Properly Efficient Solutions to Multiobjective Optimization Problems

计量

出版历程

目录

作者简介:
杨铭（1995—），女，硕士生(E-mail: yming72@163.com);高英（1982—），女，教授，博士，硕士生导师(通讯作者. E-mail: gaoyingimu@163.com).