Maeda T. On optimization problems with set-valued objective maps[J]. Appl Math Comput,2010,217:1150-1157.2000 MSC:54C05; 74P99(编辑 李德华)
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胡毓达. 多目标规划有效性理论[M]. 上海:上海科学技术出版社,1994.
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Xiang S W, Zhou Y H. On essential sets and essential components of efficient solutions for vector optimization problems[J]. J Math Anal Appl,2006,315:317-326.
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Aubin J P, Ekeland I. Applied Nonlinear Analysis[M]. New York:John Wiley & Sons,1984.
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Huang N J, Li J, Wu S Y. Optimality conditions for vector optimization oroblems[J]. J Optim Theory Appl,2009,142:323-342.
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Fang Y P, Huang N J. Increasing-along-rays property, vector optimization and well-posedness[J]. Math Meth Oper Res,2007,65:99-114.
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Zhang W Y, Li S J, Teo K L. Well-posedness for set optimization problems[J]. Nonlinear Anal,2009,71:3769-3778.
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Durea M, Strugariu R. Necessary optimality conditions for weak sharp minima in set-valued optimization[J]. Nonlinear Anal,2010,73:2148-2157.
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Chuong T D. Clarke coderivatives of efficient point multifunctions in parametric vector optimization[J]. Nonlinear Anal,2011,74:273-285.
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Hernández E, Marín L R, Sama M. On solutions of set-valued optimization problems[J]. Comput Math Appl,2010,60:1401-1408.
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Maeda T. On optimization problems with set-valued objective maps[J]. Appl Math Comput,2010,217:1150-1157. The Lower Semi-continuity of Solutions of Optimization Problem for Cone-continuity Maps with Set-value XIA Shun-you1, XU De-ping2 (1. Department of Mathematics and Computer, Guizhou Normal College, Guiyang 550018, Guizhou; 2. College of Information Management, Chengdu University of Technology, Chengdu 610059, Sichuan) Abstract:In this paper, we first define the essential efficient solutions and the essential weakly efficient solutions of optimization problem for cone continuity maps with set-value, and then, under the approximation condition of uniform topology we research the lower semi-continuity stability of the efficient solutions and the weakly efficient solutions of optimization problem for cone continuity maps with set-value. Employing the approach of perturbation analysis for general stability and essential stability, we show that the weakly efficient solution is essential if and only if it is approached extremely by the efficient solutions, and the results of some equivalences of lower semi-continuity for the efficient solutions and the weakly efficient solutions of optimization problem for cone continuity maps with set-value are obtained. These new outcomes generalize the relevant results of the present researches concerning with optimization problem of continuity function with single vector-value on finite dimensional space. Key words:cone-upper(lower)-semi-continuity;(weakly)efficient solution; essential(weakly)efficient solution; generic continuity 2000 MSC:54C05; 74P99(编辑 李德华)
[25]
Truong Xuan Duc Ha. The Ekeland variational principle for Henig proper minimizers and super minimizers[J]. J Math Anal Appl,2010,364:156-170.
[26]
Gutierrez C, Lopez R, Novo V. Generalized εV:py0∈F(y0),px∈F(x),py0-px∈K}为闭集,则x*为本质解,当且仅当对x*的任意邻域U,存在(-overx)∈S(F)∩U,使得:对任意p(-overx)∈F((-overx))∩E(F(X))有F-1(p(-overx))∩(X\ 参考文献 [1] Yu J. Essential weak efficient solution in multi-objective optimization problems[J]. J Math Anal Appl,1992,166:211-214.
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Xiang S W, Zhou Y H. Continuity properties of solutions of vector optimization[J]. Nonlinear Anal,2006,64:2496-2506.
Luc D T. Theory of Vector Optimization[M]. Berlin:Springer-Verlag,1989.
[31]
Klein E, Thompson A C. Theory of Correspondences[M]. New York:John Wiley & Sons,1984.
[32]
Fort M K Jr. Points of continuity of semi-continuous functions[J]. Publ Math Debrecen,1951,2:100-102.
[33]
胡毓达. 多目标规划有效性理论[M]. 上海:上海科学技术出版社,1994.
[34]
Xiang S W, Zhou Y H. On essential sets and essential components of efficient solutions for vector optimization problems[J]. J Math Anal Appl,2006,315:317-326.
[35]
Aubin J P, Ekeland I. Applied Nonlinear Analysis[M]. New York:John Wiley & Sons,1984.
[36]
Huang N J, Li J, Wu S Y. Optimality conditions for vector optimization oroblems[J]. J Optim Theory Appl,2009,142:323-342.
[37]
Fang Y P, Huang N J. Increasing-along-rays property, vector optimization and well-posedness[J]. Math Meth Oper Res,2007,65:99-114.
[38]
Zhang W Y, Li S J, Teo K L. Well-posedness for set optimization problems[J]. Nonlinear Anal,2009,71:3769-3778.
[39]
Durea M, Strugariu R. Necessary optimality conditions for weak sharp minima in set-valued optimization[J]. Nonlinear Anal,2010,73:2148-2157.
[40]
Chuong T D. Clarke coderivatives of efficient point multifunctions in parametric vector optimization[J]. Nonlinear Anal,2011,74:273-285.
[41]
Hernández E, Marín L R, Sama M. On solutions of set-valued optimization problems[J]. Comput Math Appl,2010,60:1401-1408.
[42]
Gutierrez C, Jimenez B, Novo V, et al. Strict approximate solutions in set-valued optimization with applications to the approximate Ekeland variational principle[J]. Nonlinear Anal,2010,73:3842-3855.
