-
Previous Article
Cardinality constrained portfolio selection problem: A completely positive programming approach
- JIMO Home
- This Issue
-
Next Article
Managing risk and disruption in production-inventory and supply chain systems: A review
$E$-super efficiency of set-valued optimization problems involving improvement sets
1. | College of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China |
2. | Department of Mathematics, Chongqing Normal University, Chongqing 400047 |
3. | College of Mathematics Science, Chongqing normal University, Chongqing 400047, China |
References:
[1] |
H. P. Benson, An improved definition of proper efficiency for vector maximization with respect to cones,, J. Math. Anal. Appl., 71 (1979), 232.
doi: 10.1016/0022-247X(79)90226-9. |
[2] |
J. M. Borwein and D. M. Zhuang, Super efficiency in vector optimization,, Trans. Am. Math. Soc., 338 (1993), 105.
doi: 10.1090/S0002-9947-1993-1098432-5. |
[3] |
Y. H. Cheng and W. T. Fu, Strong efficiency in a locally convex space,, Math. Methods Oper. Res., 50 (1999), 373.
doi: 10.1007/s001860050076. |
[4] |
M. Chicco, F. Mignanego, L. Pusillo and S. Tijs, Vector optimization problems via improvement sets,, J. Optim. Theory Appl., 150 (2011), 516.
doi: 10.1007/s10957-011-9851-1. |
[5] |
A. M. Geoffrion, Proper efficiency and the theory of vector maximization,, J. Math. Anal. Appl., 22 (1968), 618.
doi: 10.1016/0022-247X(68)90201-1. |
[6] |
C. Gutiérrez, B. Jiménez and V. Novo, Improvement sets and vector optimization,, Eur. J. Oper. Res., 223 (2012), 304. Google Scholar |
[7] |
M. I. Henig, Proper efficiency with respect to cones,, J. Optim. Theory Appl., 36 (1982), 387.
doi: 10.1007/BF00934353. |
[8] |
H. Kuhn and A. Tucker, Nonlinear programming,, in Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, (1950), 481.
|
[9] |
S. S. Kutateladze, Convex $\epsilon$-programming,, Soviet Math. Dokl., 20 (1979), 391. Google Scholar |
[10] |
T. Y. Li, Y. H. Xu and C. X. Zhu, $\varepsilon$-Strictly efficient solutions of vector optimization problems with set-valued maps,, Asia. Pacific. J. Oper. Res., 24 (2007), 841.
doi: 10.1142/S0217595907001577. |
[11] |
Z. M. Li, A theorem of the alternative and its application to the optimization of set-valued maps,, J. Optim. Theory Appl., 100 (1999), 365.
doi: 10.1023/A:1021786303883. |
[12] |
A. Mehra, Super efficiency in vector optimization with nearly convexlike set-valued maps,, J. Math. Anal. Appl., 276 (2002), 815.
doi: 10.1016/S0022-247X(02)00452-3. |
[13] |
Q. S. Qiu and W. T. Fu, The connectedness of the super efficient solution sets of the optimization problem for a set-valued mapping,, J. Sys. Sci. & Math. Scis., 22 (2002), 107.
|
[14] |
W. D. Rong and Y. N. Wu, Characterizations of super efficiency in cone-convexlike vector optimization with set-valued maps,, Math. Methods Oper. Res., 48 (1998), 247.
doi: 10.1007/s001860050026. |
[15] |
W. D. Rong and Y. N. Wu, $\epsilon$-Weak minimal solutions of vector optimization problems with set-valued maps,, J. Optim. Theory Appl., 106 (2000), 569.
doi: 10.1023/A:1004657412928. |
[16] |
L. A. Tuan, $\varepsilon$-Optimality conditions for vector optimization problems with set-valued maps,, Numer. Func. Anal. Optim., 31 (2010), 78.
doi: 10.1080/01630560903499845. |
[17] |
L. Y. Xia and J. H. Qiu, Superefficiency in vector optimization with nearly subconvexlike set-valued maps,, J. Optim. Theory Appl., 136 (2008), 125.
doi: 10.1007/s10957-007-9291-0. |
[18] |
Y. H. Xu and S. Y. Liu, Super efficiency in the nearly cone-subconvexlike vector optimization with set-valued functions,, Acta. Math. Sci. B, 25 (2005), 152.
|
[19] |
X. M. Yang, D. Li and S. Y. Wang, Near-subconvexlikeness in vector optimization with set-valued functions,, J. Optim. Theory Appl., 110 (2001), 413.
doi: 10.1023/A:1017535631418. |
[20] |
C. Zălinescu, Convex Analysis in General Vector Spaces,, World Scientific, (2002).
doi: 10.1142/9789812777096. |
[21] |
K. Q. Zhao and X. M. Yang, $E$-proper saddle points and $E$-proper duality in vector optimization with set-valued maps,, Taiwan. J. Math., 18 (2014), 483.
doi: 10.11650/tjm.18.2014.3473. |
[22] |
K. Q. Zhao and X. M. Yang, $E$-Benson proper efficiency in vector optimization,, Optimization, 64 (2015), 739.
doi: 10.1080/02331934.2013.798321. |
[23] |
K. Q. Zhao and X. M. Yang, Characterizations of the $E$-Benson proper efficiency in vector optimization problems,, Numer. Algebr. Control. Optim., 3 (2013), 643.
doi: 10.3934/naco.2013.3.643. |
[24] |
K. Q. Zhao, X. M. Yang and J. W. Peng, Weak $E$-optimal solution in vector optimization,, Taiwan. J. Math., 17 (2013), 1287.
|
[25] |
X. Y. Zheng, Proper efficiency in locally convex topological vector spaces,, J. Optim. Theory Appl., 94 (1997), 469.
doi: 10.1023/A:1022648115446. |
[26] |
Z. A. Zhou and J. W. Peng, Scalarization of set-valued optimization problems with generalization cone subconvexlikeness in real ordered linear spaces,, J. Optim. Theory Appl., 154 (2012), 830.
doi: 10.1007/s10957-012-0045-2. |
show all references
References:
[1] |
H. P. Benson, An improved definition of proper efficiency for vector maximization with respect to cones,, J. Math. Anal. Appl., 71 (1979), 232.
doi: 10.1016/0022-247X(79)90226-9. |
[2] |
J. M. Borwein and D. M. Zhuang, Super efficiency in vector optimization,, Trans. Am. Math. Soc., 338 (1993), 105.
doi: 10.1090/S0002-9947-1993-1098432-5. |
[3] |
Y. H. Cheng and W. T. Fu, Strong efficiency in a locally convex space,, Math. Methods Oper. Res., 50 (1999), 373.
doi: 10.1007/s001860050076. |
[4] |
M. Chicco, F. Mignanego, L. Pusillo and S. Tijs, Vector optimization problems via improvement sets,, J. Optim. Theory Appl., 150 (2011), 516.
doi: 10.1007/s10957-011-9851-1. |
[5] |
A. M. Geoffrion, Proper efficiency and the theory of vector maximization,, J. Math. Anal. Appl., 22 (1968), 618.
doi: 10.1016/0022-247X(68)90201-1. |
[6] |
C. Gutiérrez, B. Jiménez and V. Novo, Improvement sets and vector optimization,, Eur. J. Oper. Res., 223 (2012), 304. Google Scholar |
[7] |
M. I. Henig, Proper efficiency with respect to cones,, J. Optim. Theory Appl., 36 (1982), 387.
doi: 10.1007/BF00934353. |
[8] |
H. Kuhn and A. Tucker, Nonlinear programming,, in Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, (1950), 481.
|
[9] |
S. S. Kutateladze, Convex $\epsilon$-programming,, Soviet Math. Dokl., 20 (1979), 391. Google Scholar |
[10] |
T. Y. Li, Y. H. Xu and C. X. Zhu, $\varepsilon$-Strictly efficient solutions of vector optimization problems with set-valued maps,, Asia. Pacific. J. Oper. Res., 24 (2007), 841.
doi: 10.1142/S0217595907001577. |
[11] |
Z. M. Li, A theorem of the alternative and its application to the optimization of set-valued maps,, J. Optim. Theory Appl., 100 (1999), 365.
doi: 10.1023/A:1021786303883. |
[12] |
A. Mehra, Super efficiency in vector optimization with nearly convexlike set-valued maps,, J. Math. Anal. Appl., 276 (2002), 815.
doi: 10.1016/S0022-247X(02)00452-3. |
[13] |
Q. S. Qiu and W. T. Fu, The connectedness of the super efficient solution sets of the optimization problem for a set-valued mapping,, J. Sys. Sci. & Math. Scis., 22 (2002), 107.
|
[14] |
W. D. Rong and Y. N. Wu, Characterizations of super efficiency in cone-convexlike vector optimization with set-valued maps,, Math. Methods Oper. Res., 48 (1998), 247.
doi: 10.1007/s001860050026. |
[15] |
W. D. Rong and Y. N. Wu, $\epsilon$-Weak minimal solutions of vector optimization problems with set-valued maps,, J. Optim. Theory Appl., 106 (2000), 569.
doi: 10.1023/A:1004657412928. |
[16] |
L. A. Tuan, $\varepsilon$-Optimality conditions for vector optimization problems with set-valued maps,, Numer. Func. Anal. Optim., 31 (2010), 78.
doi: 10.1080/01630560903499845. |
[17] |
L. Y. Xia and J. H. Qiu, Superefficiency in vector optimization with nearly subconvexlike set-valued maps,, J. Optim. Theory Appl., 136 (2008), 125.
doi: 10.1007/s10957-007-9291-0. |
[18] |
Y. H. Xu and S. Y. Liu, Super efficiency in the nearly cone-subconvexlike vector optimization with set-valued functions,, Acta. Math. Sci. B, 25 (2005), 152.
|
[19] |
X. M. Yang, D. Li and S. Y. Wang, Near-subconvexlikeness in vector optimization with set-valued functions,, J. Optim. Theory Appl., 110 (2001), 413.
doi: 10.1023/A:1017535631418. |
[20] |
C. Zălinescu, Convex Analysis in General Vector Spaces,, World Scientific, (2002).
doi: 10.1142/9789812777096. |
[21] |
K. Q. Zhao and X. M. Yang, $E$-proper saddle points and $E$-proper duality in vector optimization with set-valued maps,, Taiwan. J. Math., 18 (2014), 483.
doi: 10.11650/tjm.18.2014.3473. |
[22] |
K. Q. Zhao and X. M. Yang, $E$-Benson proper efficiency in vector optimization,, Optimization, 64 (2015), 739.
doi: 10.1080/02331934.2013.798321. |
[23] |
K. Q. Zhao and X. M. Yang, Characterizations of the $E$-Benson proper efficiency in vector optimization problems,, Numer. Algebr. Control. Optim., 3 (2013), 643.
doi: 10.3934/naco.2013.3.643. |
[24] |
K. Q. Zhao, X. M. Yang and J. W. Peng, Weak $E$-optimal solution in vector optimization,, Taiwan. J. Math., 17 (2013), 1287.
|
[25] |
X. Y. Zheng, Proper efficiency in locally convex topological vector spaces,, J. Optim. Theory Appl., 94 (1997), 469.
doi: 10.1023/A:1022648115446. |
[26] |
Z. A. Zhou and J. W. Peng, Scalarization of set-valued optimization problems with generalization cone subconvexlikeness in real ordered linear spaces,, J. Optim. Theory Appl., 154 (2012), 830.
doi: 10.1007/s10957-012-0045-2. |
[1] |
Guolin Yu. Global proper efficiency and vector optimization with cone-arcwise connected set-valued maps. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 35-44. doi: 10.3934/naco.2016.6.35 |
[2] |
Dante Carrasco-Olivera, Roger Metzger Alvan, Carlos Arnoldo Morales Rojas. Topological entropy for set-valued maps. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3461-3474. doi: 10.3934/dcdsb.2015.20.3461 |
[3] |
Zhenhua Peng, Zhongping Wan, Weizhi Xiong. Sensitivity analysis in set-valued optimization under strictly minimal efficiency. Evolution Equations & Control Theory, 2017, 6 (3) : 427-436. doi: 10.3934/eect.2017022 |
[4] |
Yihong Xu, Zhenhua Peng. Higher-order sensitivity analysis in set-valued optimization under Henig efficiency. Journal of Industrial & Management Optimization, 2017, 13 (1) : 313-327. doi: 10.3934/jimo.2016019 |
[5] |
Ying Gao, Xinmin Yang, Jin Yang, Hong Yan. Scalarizations and Lagrange multipliers for approximate solutions in the vector optimization problems with set-valued maps. Journal of Industrial & Management Optimization, 2015, 11 (2) : 673-683. doi: 10.3934/jimo.2015.11.673 |
[6] |
Kequan Zhao, Xinmin Yang. Characterizations of the $E$-Benson proper efficiency in vector optimization problems. Numerical Algebra, Control & Optimization, 2013, 3 (4) : 643-653. doi: 10.3934/naco.2013.3.643 |
[7] |
Roger Metzger, Carlos Arnoldo Morales Rojas, Phillipe Thieullen. Topological stability in set-valued dynamics. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1965-1975. doi: 10.3934/dcdsb.2017115 |
[8] |
Geng-Hua Li, Sheng-Jie Li. Unified optimality conditions for set-valued optimizations. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1101-1116. doi: 10.3934/jimo.2018087 |
[9] |
Tao Chen, Yunping Jiang, Gaofei Zhang. No invariant line fields on escaping sets of the family $\lambda e^{iz}+\gamma e^{-iz}$. Discrete & Continuous Dynamical Systems - A, 2013, 33 (5) : 1883-1890. doi: 10.3934/dcds.2013.33.1883 |
[10] |
Yu Zhang, Tao Chen. Minimax problems for set-valued mappings with set optimization. Numerical Algebra, Control & Optimization, 2014, 4 (4) : 327-340. doi: 10.3934/naco.2014.4.327 |
[11] |
Caili Sang, Zhen Chen. $ E $-eigenvalue localization sets for tensors. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-19. doi: 10.3934/jimo.2019042 |
[12] |
Qingbang Zhang, Caozong Cheng, Xuanxuan Li. Generalized minimax theorems for two set-valued mappings. Journal of Industrial & Management Optimization, 2013, 9 (1) : 1-12. doi: 10.3934/jimo.2013.9.1 |
[13] |
Sina Greenwood, Rolf Suabedissen. 2-manifolds and inverse limits of set-valued functions on intervals. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5693-5706. doi: 10.3934/dcds.2017246 |
[14] |
Mariusz Michta. Stochastic inclusions with non-continuous set-valued operators. Conference Publications, 2009, 2009 (Special) : 548-557. doi: 10.3934/proc.2009.2009.548 |
[15] |
Guolin Yu. Topological properties of Henig globally efficient solutions of set-valued problems. Numerical Algebra, Control & Optimization, 2014, 4 (4) : 309-316. doi: 10.3934/naco.2014.4.309 |
[16] |
Zengjing Chen, Yuting Lan, Gaofeng Zong. Strong law of large numbers for upper set-valued and fuzzy-set valued probability. Mathematical Control & Related Fields, 2015, 5 (3) : 435-452. doi: 10.3934/mcrf.2015.5.435 |
[17] |
Tadeusz Antczak, Najeeb Abdulaleem. Optimality conditions for $ E $-differentiable vector optimization problems with the multiple interval-valued objective function. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-19. doi: 10.3934/jimo.2019089 |
[18] |
C. R. Chen, S. J. Li. Semicontinuity of the solution set map to a set-valued weak vector variational inequality. Journal of Industrial & Management Optimization, 2007, 3 (3) : 519-528. doi: 10.3934/jimo.2007.3.519 |
[19] |
Jiawei Chen, Zhongping Wan, Liuyang Yuan. Existence of solutions and $\alpha$-well-posedness for a system of constrained set-valued variational inequalities. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 567-581. doi: 10.3934/naco.2013.3.567 |
[20] |
Benjamin Seibold, Morris R. Flynn, Aslan R. Kasimov, Rodolfo R. Rosales. Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models. Networks & Heterogeneous Media, 2013, 8 (3) : 745-772. doi: 10.3934/nhm.2013.8.745 |
2018 Impact Factor: 1.025
Tools
Metrics
Other articles
by authors
[Back to Top]