-
Previous Article
A note on the stability of a second order finite difference scheme for space fractional diffusion equations
- NACO Home
- This Issue
-
Next Article
Nonlinear scalarization with applications to Hölder continuity of approximate solutions
Topological properties of Henig globally efficient solutions of set-valued problems
1. | Institute of Applied Mathematics, Beifang University of Nationalities, Yinchuan 750021, China |
References:
[1] |
J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis. Wiley, New York, 1984.
doi: 10.1007/978-1-4612-0873-0. |
[2] |
H. P. Benson, An improved definition of proper efficiency for vector maximization with respect to cones, Journal of Mathematical Analysis and Applications, 71 (1979), 232-241.
doi: 10.1016/0022-247X(79)90226-9. |
[3] |
J. M. Borwein and D. M. Zhuang, Super efficiency in vector optimization, Trans. Amer. Math. Soc., 338 (1993), 105-122.
doi: 10.2307/2154446. |
[4] |
H. W. Corley, Optimality conditions for maximizations of set-valued functions, Journal of Optimization Theory and Applications, 54 (1987), 489-501.
doi: 10.1007/BF00940198. |
[5] |
X. H. Gong, Optimality conditions for Henig and globally proper efficient solutions with ordering cone has empty interior, Journal of Mathematical Analysis and Applications, 307 (2005), 12-31.
doi: 10.1016/j.jmaa.2004.10.001. |
[6] |
X. H. Gong, Connectedness of super efficient solution sets for set-valued maps in Banach spaces, Mathematical Methods of Operation Research, 44 (1996), 135-145.
doi: 10.1007/BF01246333. |
[7] |
X. H. Gong, Connectedness of efficient solution sets for set-valued maps in normed spaces, Journal of Optimization Theory and Applications, 83 (1994), 83-96.
doi: 10.1007/BF02191763. |
[8] |
X. H. Gong, H. B. Dong and S. Y. Wang, Optimality conditions for proper efficient solutions of vector set-valued optimization, Journal of Mathematical Analysis and Applications, 284 (2003), 332-350.
doi: 10.1016/S0022-247X(03)00360-3. |
[9] |
M. I. Henig, Proper efficiency with respect to cones, Journal of Optimization Theory and Applications, 36 (1982), 387-407.
doi: 10.1007/BF00934353. |
[10] |
J. B. Hiriart-Urruty, Images of connected sets by semicontinuous multifunctions, Journal of Mathematical Analysis and Applications, 111 (1985), 407-422.
doi: 10.1016/0022-247X(85)90225-2. |
[11] |
Z. F. Li, Benson proper efficiency in the vector optimization of set-valued maps, Journal of Optimization Theory and Applications, 98 (1998), 623-649.
doi: 10.1023/A:1022676013609. |
[12] |
Y. X. Li, Topological structure of efficient set of optimization problem so set-valued mapping, Chinese Annals of Mathematics, 15B (1994), 115-122. |
[13] |
Z. F. Li and S. Y. Wang, Connectedness of super efficient sets in vector optimization of set-valued maps, Mathematical Methods of Operation Research, 48 (1998), 207-217.
doi: 10.1007/s001860050023. |
[14] |
Z. F. Li and G, Y, Chen, Lagrangian multipliers, saddle points and duality in vector optimizaition of set-valued maps, Journal of Mathematical Analysis and Applications, 215 (1997), 297-316.
doi: 10.1006/jmaa.1997.5568. |
[15] |
P. H. Naccache, Connectedness of the set of nondominated outcomes in multicriteria optimization, Journal of Optimization Theory and Applications, 25 (1978), 459-467.
doi: 10.1007/BF00932907. |
[16] |
Q. S. Qiu and X. M. Yang, Connectedness of Henig weakly efficient solution set for set-valued optimization problems, Journal of Optimization Theory and Applications, 152 (2012), 439-449.
doi: 10.1007/s10957-011-9906-3. |
[17] |
P. H. Sach, New generalized convexity notion for set-valued maps and application to vector optimization, Journal of Optimization Theory and Applications, 125 (2005), 157-179.
doi: 10.1007/s10957-004-1716-4. |
[18] |
W. Song, Lagrangian duality for minimization of nonconvex multifunctions, Journal of Optimization Theory and Applications, 93 (1997), 167-182.
doi: 10.1023/A:1022658019642. |
[19] |
A. R. Warburton, Quasiconcave vector maximization: connectedness of the sets of Pareto-optimal and weak Pareto-optimal alternatives, Journal of Optimization Theory and Applications, 140 (1983), 537-557.
doi: 10.1007/BF00933970. |
[20] |
Yihong Xu and Xiaoshuai Song, The relationship between ic-cone-convexness and nearly cone-subconvexlikeness, Applied Mathematics Letters, 24 (2011), 1622-1624.
doi: 10.1016/j.aml.2011.04.018. |
[21] |
X. M. Yang, X. Q. Yang and G. Y. Cheng, Theorems of the alternative and optimization with set-valued maps, Journal of Optimization Theory and Applications, 107 (2000), 627-640.
doi: 10.1023/A:1004613630675. |
[22] |
Guolin Yu and Sanyang Liu, Optimality conditions of globally proper efficient solutions for set-valued optimization problem, Acta Mathematicae Applicatae Sinica, 33 (2010), 150-160. |
[23] |
Guolin Yu and Sanyang Liu, Globally proper saddle point in ic-cone-convexlike set-valued optimization problems, Act Mathematica Sinica (English Series), 25 (2009), 1921-1928.
doi: 10.1007/s10114-009-6144-9. |
show all references
References:
[1] |
J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis. Wiley, New York, 1984.
doi: 10.1007/978-1-4612-0873-0. |
[2] |
H. P. Benson, An improved definition of proper efficiency for vector maximization with respect to cones, Journal of Mathematical Analysis and Applications, 71 (1979), 232-241.
doi: 10.1016/0022-247X(79)90226-9. |
[3] |
J. M. Borwein and D. M. Zhuang, Super efficiency in vector optimization, Trans. Amer. Math. Soc., 338 (1993), 105-122.
doi: 10.2307/2154446. |
[4] |
H. W. Corley, Optimality conditions for maximizations of set-valued functions, Journal of Optimization Theory and Applications, 54 (1987), 489-501.
doi: 10.1007/BF00940198. |
[5] |
X. H. Gong, Optimality conditions for Henig and globally proper efficient solutions with ordering cone has empty interior, Journal of Mathematical Analysis and Applications, 307 (2005), 12-31.
doi: 10.1016/j.jmaa.2004.10.001. |
[6] |
X. H. Gong, Connectedness of super efficient solution sets for set-valued maps in Banach spaces, Mathematical Methods of Operation Research, 44 (1996), 135-145.
doi: 10.1007/BF01246333. |
[7] |
X. H. Gong, Connectedness of efficient solution sets for set-valued maps in normed spaces, Journal of Optimization Theory and Applications, 83 (1994), 83-96.
doi: 10.1007/BF02191763. |
[8] |
X. H. Gong, H. B. Dong and S. Y. Wang, Optimality conditions for proper efficient solutions of vector set-valued optimization, Journal of Mathematical Analysis and Applications, 284 (2003), 332-350.
doi: 10.1016/S0022-247X(03)00360-3. |
[9] |
M. I. Henig, Proper efficiency with respect to cones, Journal of Optimization Theory and Applications, 36 (1982), 387-407.
doi: 10.1007/BF00934353. |
[10] |
J. B. Hiriart-Urruty, Images of connected sets by semicontinuous multifunctions, Journal of Mathematical Analysis and Applications, 111 (1985), 407-422.
doi: 10.1016/0022-247X(85)90225-2. |
[11] |
Z. F. Li, Benson proper efficiency in the vector optimization of set-valued maps, Journal of Optimization Theory and Applications, 98 (1998), 623-649.
doi: 10.1023/A:1022676013609. |
[12] |
Y. X. Li, Topological structure of efficient set of optimization problem so set-valued mapping, Chinese Annals of Mathematics, 15B (1994), 115-122. |
[13] |
Z. F. Li and S. Y. Wang, Connectedness of super efficient sets in vector optimization of set-valued maps, Mathematical Methods of Operation Research, 48 (1998), 207-217.
doi: 10.1007/s001860050023. |
[14] |
Z. F. Li and G, Y, Chen, Lagrangian multipliers, saddle points and duality in vector optimizaition of set-valued maps, Journal of Mathematical Analysis and Applications, 215 (1997), 297-316.
doi: 10.1006/jmaa.1997.5568. |
[15] |
P. H. Naccache, Connectedness of the set of nondominated outcomes in multicriteria optimization, Journal of Optimization Theory and Applications, 25 (1978), 459-467.
doi: 10.1007/BF00932907. |
[16] |
Q. S. Qiu and X. M. Yang, Connectedness of Henig weakly efficient solution set for set-valued optimization problems, Journal of Optimization Theory and Applications, 152 (2012), 439-449.
doi: 10.1007/s10957-011-9906-3. |
[17] |
P. H. Sach, New generalized convexity notion for set-valued maps and application to vector optimization, Journal of Optimization Theory and Applications, 125 (2005), 157-179.
doi: 10.1007/s10957-004-1716-4. |
[18] |
W. Song, Lagrangian duality for minimization of nonconvex multifunctions, Journal of Optimization Theory and Applications, 93 (1997), 167-182.
doi: 10.1023/A:1022658019642. |
[19] |
A. R. Warburton, Quasiconcave vector maximization: connectedness of the sets of Pareto-optimal and weak Pareto-optimal alternatives, Journal of Optimization Theory and Applications, 140 (1983), 537-557.
doi: 10.1007/BF00933970. |
[20] |
Yihong Xu and Xiaoshuai Song, The relationship between ic-cone-convexness and nearly cone-subconvexlikeness, Applied Mathematics Letters, 24 (2011), 1622-1624.
doi: 10.1016/j.aml.2011.04.018. |
[21] |
X. M. Yang, X. Q. Yang and G. Y. Cheng, Theorems of the alternative and optimization with set-valued maps, Journal of Optimization Theory and Applications, 107 (2000), 627-640.
doi: 10.1023/A:1004613630675. |
[22] |
Guolin Yu and Sanyang Liu, Optimality conditions of globally proper efficient solutions for set-valued optimization problem, Acta Mathematicae Applicatae Sinica, 33 (2010), 150-160. |
[23] |
Guolin Yu and Sanyang Liu, Globally proper saddle point in ic-cone-convexlike set-valued optimization problems, Act Mathematica Sinica (English Series), 25 (2009), 1921-1928.
doi: 10.1007/s10114-009-6144-9. |
[1] |
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 |
[2] |
Yihong Xu, Zhenhua Peng. Higher-order sensitivity analysis in set-valued optimization under Henig efficiency. Journal of Industrial and Management Optimization, 2017, 13 (1) : 313-327. doi: 10.3934/jimo.2016019 |
[3] |
Zhenhua Peng, Zhongping Wan, Weizhi Xiong. Sensitivity analysis in set-valued optimization under strictly minimal efficiency. Evolution Equations and Control Theory, 2017, 6 (3) : 427-436. doi: 10.3934/eect.2017022 |
[4] |
Kequan Zhao, Xinmin Yang. Characterizations of the $E$-Benson proper efficiency in vector optimization problems. Numerical Algebra, Control and Optimization, 2013, 3 (4) : 643-653. doi: 10.3934/naco.2013.3.643 |
[5] |
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 |
[6] |
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 |
[7] |
Roger Metzger, Carlos Arnoldo Morales Rojas, Phillipe Thieullen. Topological stability in set-valued dynamics. Discrete and Continuous Dynamical Systems - B, 2017, 22 (5) : 1965-1975. doi: 10.3934/dcdsb.2017115 |
[8] |
Dante Carrasco-Olivera, Roger Metzger Alvan, Carlos Arnoldo Morales Rojas. Topological entropy for set-valued maps. Discrete and Continuous Dynamical Systems - B, 2015, 20 (10) : 3461-3474. doi: 10.3934/dcdsb.2015.20.3461 |
[9] |
Yu Zhang, Tao Chen. Minimax problems for set-valued mappings with set optimization. Numerical Algebra, Control and Optimization, 2014, 4 (4) : 327-340. doi: 10.3934/naco.2014.4.327 |
[10] |
Hong-Zhi Wei, Chun-Rong Chen. Three concepts of robust efficiency for uncertain multiobjective optimization problems via set order relations. Journal of Industrial and Management Optimization, 2019, 15 (2) : 705-721. doi: 10.3934/jimo.2018066 |
[11] |
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 |
[12] |
Qilin Wang, Liu He, Shengjie Li. Higher-order weak radial epiderivatives and non-convex set-valued optimization problems. Journal of Industrial and Management Optimization, 2019, 15 (2) : 465-480. doi: 10.3934/jimo.2018051 |
[13] |
T.C. Edwin Cheng, Yunan Wu. Henig efficiency of a multi-criterion supply-demand network equilibrium model. Journal of Industrial and Management Optimization, 2006, 2 (3) : 269-286. doi: 10.3934/jimo.2006.2.269 |
[14] |
Geng-Hua Li, Sheng-Jie Li. Unified optimality conditions for set-valued optimizations. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1101-1116. doi: 10.3934/jimo.2018087 |
[15] |
Kendry J. Vivas, Víctor F. Sirvent. Metric entropy for set-valued maps. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022010 |
[16] |
Qingbang Zhang, Caozong Cheng, Xuanxuan Li. Generalized minimax theorems for two set-valued mappings. Journal of Industrial and Management Optimization, 2013, 9 (1) : 1-12. doi: 10.3934/jimo.2013.9.1 |
[17] |
Sina Greenwood, Rolf Suabedissen. 2-manifolds and inverse limits of set-valued functions on intervals. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5693-5706. doi: 10.3934/dcds.2017246 |
[18] |
Mariusz Michta. Stochastic inclusions with non-continuous set-valued operators. Conference Publications, 2009, 2009 (Special) : 548-557. doi: 10.3934/proc.2009.2009.548 |
[19] |
Zengjing Chen, Yuting Lan, Gaofeng Zong. Strong law of large numbers for upper set-valued and fuzzy-set valued probability. Mathematical Control and Related Fields, 2015, 5 (3) : 435-452. doi: 10.3934/mcrf.2015.5.435 |
[20] |
Michele Campiti. Korovkin-type approximation of set-valued and vector-valued functions. Mathematical Foundations of Computing, 2022, 5 (3) : 231-239. doi: 10.3934/mfc.2021032 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]