-
Previous Article
Dampening bullwhip effect of order-up-to inventory strategies via an optimal control method
- NACO Home
- This Issue
-
Next Article
Error bounds for symmetric cone complementarity problems
Characterizations of the $E$-Benson proper efficiency in vector optimization problems
1. | College of Mathematics Science, Chongqing Normal University, Chongqing 401331, China, 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), 232-241.
doi: 10.1016/0022-247X(79)90226-9. |
[2] |
J. Borwein, Proper efficient points for maximizations with respect to cones, SIAM. J. Control and Optim., 15 (1977), 57-63. |
[3] |
G. Y. Chen and W. D. Rong, Characterizations of the Benson proper efficiency for nonconvex vector optimization, J. Optim. Theory Appl., 98 (1998), 365-384.
doi: 10.1023/A:1022689517921. |
[4] |
G. Y. Chen, X. X. Huang and X. Q. Yang, "Vector Optimization. Lecture Notes in Economics and Mathematical Sciences, 541," Springer, Berlin, 2005. |
[5] |
M. Chicco, F. Mignanego, L. Pusillo and S. Tijs, Vector optimization problems via improvement sets, J. Optim. Theory Appl., 150 (2011), 516-529.
doi: 10.1007/s10957-011-9851-1. |
[6] |
M. Ehrgott, "Multicriteria Optimization," Springer, Berlin, 2005. |
[7] |
Y. Gao and X. M. Yang, Optimality conditions for approximate solutions of vector optimization problems, J. Ind. Manag. Optim., 7 (2011), 483-496.
doi: 10.3934/jimo.2011.7.483. |
[8] |
A. M. Geffrion, Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl., 22 (1968), 618-630. |
[9] |
B. A. Ghaznavi-ghosoni, E. Khorram and M. Soleimani-damaneh, Scalarization for characterization of approximate strong/weak/proper efficiency in multiobjective optimization, Optimization, 62 (2013), 703-720.
doi: 10.1080/02331934.2012.668190. |
[10] |
C. Gutiérrez, B. Jiménez and V. Novo, Improvement sets and vector optimization, Eur. J. Oper. Res., 223 (2012), 304-311. |
[11] |
C. Gutiérrez, B. Jiménez and V. Novo, A unified approach and optimality conditions for approximate solutions of vector optimization problems, SIAM J. Optim., 17 (2006), 688-710. |
[12] |
C. Gutiérrez, L. Huerga and V. Novo, Scalarization and saddle points of approximate proper solutions in nearly subconvexlike vector optimization problems, J. Math. Anal. Appl., 389 (2012), 1046-1058.
doi: 10.1016/j.jmaa.2011.12.050. |
[13] |
M. I. Henig, Proper efficiency with respect to cones, J. Optim. Theory Appl., 36 (1982), 387-407.
doi: 10.1007/BF00934353. |
[14] |
J. Jahn, "Vector Optimization. Theory, Applications, and Extensions," Springer, Berlin, 2004. |
[15] |
Z. F. Li, Benson proper efficiency in the vector optimization of set-valued maps, J. Optim. Theory Appl., 98 (1998), 623-649.
doi: 10.1023/A:1022676013609. |
[16] |
J. C. Liu, ε-Properly efficient solutions to nondifferentiable multiobjective programming problems, Appl. Math. Lett., 12 (1999), 109-113.
doi: 10.1016/S0893-9659(99)00087-7. |
[17] |
D. T. Luc, "Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Sciences, 319," Springer, Berlin, 1988. |
[18] |
W. D. Rong and Y. Ma, ε-Properly efficient solutions of vector optimization problems with set-valued maps, OR Transactions, 4 (2000), 21-32. |
[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), 413-427.
doi: 10.1023/A:1017535631418. |
[20] |
X. M. Yang, X. Q. Yang and G. Y. Chen, Theorems of the alternative and optimization with set-valued maps, J. Optim. Theory Appl., 107 (2000), 627-640.
doi: 10.1023/A:1004613630675. |
[21] |
K. Q. Zhao and X. M. Yang, E-Benson proper efficiency in vector optimization, Optimization, doi:10.1080/02331934.2013.798321, 2013.
doi: 10.1080/02331934.2013.798321. |
[22] |
K. Q. Zhao, X. M. Yang and J. W. Peng, Weak E-Optimal solution in vector optimization, Taiwan. J. Math., 17 (2013), 1287-1302. |
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), 232-241.
doi: 10.1016/0022-247X(79)90226-9. |
[2] |
J. Borwein, Proper efficient points for maximizations with respect to cones, SIAM. J. Control and Optim., 15 (1977), 57-63. |
[3] |
G. Y. Chen and W. D. Rong, Characterizations of the Benson proper efficiency for nonconvex vector optimization, J. Optim. Theory Appl., 98 (1998), 365-384.
doi: 10.1023/A:1022689517921. |
[4] |
G. Y. Chen, X. X. Huang and X. Q. Yang, "Vector Optimization. Lecture Notes in Economics and Mathematical Sciences, 541," Springer, Berlin, 2005. |
[5] |
M. Chicco, F. Mignanego, L. Pusillo and S. Tijs, Vector optimization problems via improvement sets, J. Optim. Theory Appl., 150 (2011), 516-529.
doi: 10.1007/s10957-011-9851-1. |
[6] |
M. Ehrgott, "Multicriteria Optimization," Springer, Berlin, 2005. |
[7] |
Y. Gao and X. M. Yang, Optimality conditions for approximate solutions of vector optimization problems, J. Ind. Manag. Optim., 7 (2011), 483-496.
doi: 10.3934/jimo.2011.7.483. |
[8] |
A. M. Geffrion, Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl., 22 (1968), 618-630. |
[9] |
B. A. Ghaznavi-ghosoni, E. Khorram and M. Soleimani-damaneh, Scalarization for characterization of approximate strong/weak/proper efficiency in multiobjective optimization, Optimization, 62 (2013), 703-720.
doi: 10.1080/02331934.2012.668190. |
[10] |
C. Gutiérrez, B. Jiménez and V. Novo, Improvement sets and vector optimization, Eur. J. Oper. Res., 223 (2012), 304-311. |
[11] |
C. Gutiérrez, B. Jiménez and V. Novo, A unified approach and optimality conditions for approximate solutions of vector optimization problems, SIAM J. Optim., 17 (2006), 688-710. |
[12] |
C. Gutiérrez, L. Huerga and V. Novo, Scalarization and saddle points of approximate proper solutions in nearly subconvexlike vector optimization problems, J. Math. Anal. Appl., 389 (2012), 1046-1058.
doi: 10.1016/j.jmaa.2011.12.050. |
[13] |
M. I. Henig, Proper efficiency with respect to cones, J. Optim. Theory Appl., 36 (1982), 387-407.
doi: 10.1007/BF00934353. |
[14] |
J. Jahn, "Vector Optimization. Theory, Applications, and Extensions," Springer, Berlin, 2004. |
[15] |
Z. F. Li, Benson proper efficiency in the vector optimization of set-valued maps, J. Optim. Theory Appl., 98 (1998), 623-649.
doi: 10.1023/A:1022676013609. |
[16] |
J. C. Liu, ε-Properly efficient solutions to nondifferentiable multiobjective programming problems, Appl. Math. Lett., 12 (1999), 109-113.
doi: 10.1016/S0893-9659(99)00087-7. |
[17] |
D. T. Luc, "Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Sciences, 319," Springer, Berlin, 1988. |
[18] |
W. D. Rong and Y. Ma, ε-Properly efficient solutions of vector optimization problems with set-valued maps, OR Transactions, 4 (2000), 21-32. |
[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), 413-427.
doi: 10.1023/A:1017535631418. |
[20] |
X. M. Yang, X. Q. Yang and G. Y. Chen, Theorems of the alternative and optimization with set-valued maps, J. Optim. Theory Appl., 107 (2000), 627-640.
doi: 10.1023/A:1004613630675. |
[21] |
K. Q. Zhao and X. M. Yang, E-Benson proper efficiency in vector optimization, Optimization, doi:10.1080/02331934.2013.798321, 2013.
doi: 10.1080/02331934.2013.798321. |
[22] |
K. Q. Zhao, X. M. Yang and J. W. Peng, Weak E-Optimal solution in vector optimization, Taiwan. J. Math., 17 (2013), 1287-1302. |
[1] |
Marius Durea, Elena-Andreea Florea, Radu Strugariu. Henig proper efficiency in vector optimization with variable ordering structure. Journal of Industrial and Management Optimization, 2019, 15 (2) : 791-815. doi: 10.3934/jimo.2018071 |
[2] |
Guolin Yu. Global proper efficiency and vector optimization with cone-arcwise connected set-valued maps. Numerical Algebra, Control and Optimization, 2016, 6 (1) : 35-44. doi: 10.3934/naco.2016.6.35 |
[3] |
Zhiang Zhou, Xinmin Yang, Kequan Zhao. $E$-super efficiency of set-valued optimization problems involving improvement sets. Journal of Industrial and Management Optimization, 2016, 12 (3) : 1031-1039. doi: 10.3934/jimo.2016.12.1031 |
[4] |
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 and Management Optimization, 2015, 11 (2) : 673-683. doi: 10.3934/jimo.2015.11.673 |
[5] |
Tadeusz Antczak, Najeeb Abdulaleem. Optimality conditions for $ E $-differentiable vector optimization problems with the multiple interval-valued objective function. Journal of Industrial and Management Optimization, 2020, 16 (6) : 2971-2989. doi: 10.3934/jimo.2019089 |
[6] |
Aleksandar Jović. Saddle-point type optimality criteria, duality and a new approach for solving nonsmooth fractional continuous-time programming problems. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022025 |
[7] |
Caiping Liu, Heungwing Lee. Lagrange multiplier rules for approximate solutions in vector optimization. Journal of Industrial and Management Optimization, 2012, 8 (3) : 749-764. doi: 10.3934/jimo.2012.8.749 |
[8] |
Najeeb Abdulaleem. Optimality and duality for $ E $-differentiable multiobjective programming problems involving $ E $-type Ⅰ functions. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022004 |
[9] |
Xinmin Yang. On symmetric and self duality in vector optimization problem. Journal of Industrial and Management Optimization, 2011, 7 (3) : 523-529. doi: 10.3934/jimo.2011.7.523 |
[10] |
Manxue You, Shengjie Li. Perturbation of Image and conjugate duality for vector optimization. Journal of Industrial and Management Optimization, 2022, 18 (2) : 731-745. doi: 10.3934/jimo.2020176 |
[11] |
Karla L. Cortez, Javier F. Rosenblueth. Normality and uniqueness of Lagrange multipliers. Discrete and Continuous Dynamical Systems, 2018, 38 (6) : 3169-3188. doi: 10.3934/dcds.2018138 |
[12] |
Najeeb Abdulaleem. $ V $-$ E $-invexity in $ E $-differentiable multiobjective programming. Numerical Algebra, Control and Optimization, 2022, 12 (2) : 427-443. doi: 10.3934/naco.2021014 |
[13] |
Radu Ioan Boţ, Sorin-Mihai Grad. On linear vector optimization duality in infinite-dimensional spaces. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 407-415. doi: 10.3934/naco.2011.1.407 |
[14] |
Jiawei Chen, Shengjie Li, Jen-Chih Yao. Vector-valued separation functions and constrained vector optimization problems: optimality and saddle points. Journal of Industrial and Management Optimization, 2020, 16 (2) : 707-724. doi: 10.3934/jimo.2018174 |
[15] |
Takeshi Fukao, Nobuyuki Kenmochi. Abstract theory of variational inequalities and Lagrange multipliers. Conference Publications, 2013, 2013 (special) : 237-246. doi: 10.3934/proc.2013.2013.237 |
[16] |
Tao Jie, Gao Yan. Computing shadow prices with multiple Lagrange multipliers. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2307-2329. doi: 10.3934/jimo.2020070 |
[17] |
Qiusheng Qiu, Xinmin Yang. Scalarization of approximate solution for vector equilibrium problems. Journal of Industrial and Management Optimization, 2013, 9 (1) : 143-151. doi: 10.3934/jimo.2013.9.143 |
[18] |
Annamaria Barbagallo, Rosalba Di Vincenzo, Stéphane Pia. On strong Lagrange duality for weighted traffic equilibrium problem. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1097-1113. doi: 10.3934/dcds.2011.31.1097 |
[19] |
Regina Sandra Burachik, Alex Rubinov. On the absence of duality gap for Lagrange-type functions. Journal of Industrial and Management Optimization, 2005, 1 (1) : 33-38. doi: 10.3934/jimo.2005.1.33 |
[20] |
Baoxiang Wang. E-Besov spaces and dissipative equations. Communications on Pure and Applied Analysis, 2004, 3 (4) : 883-919. doi: 10.3934/cpaa.2004.3.883 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]