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Global proper efficiency and vector optimization with cone-arcwise connected set-valued maps
1. | Institute of Applied Mathematics, Beifang University of Nationalities, Yinchuan 750021 |
References:
[1] |
M. Avriel and I. Zang , Generalized arcwise-connected functions and characterizations of local-global minimum properties, Journal of Optimization Theory and Applications, 32 (1980), 407-425.
doi: 10.1007/BF00934030. |
[2] |
J. Baier and J. Jahn, On subdifferentials of set-valued maps, Journal of Optimization Theory and Applications, 100 (1980), 233-240.
doi: 10.1023/A:1021733402240. |
[3] |
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. |
[4] |
J. M. Borwein and D. M. Zhuang, Super efficiency in vector optimiation, Transactions of the American Mathematical Society, 338 (1993), 105-122.
doi: 10.2307/2154446. |
[5] |
Y. H. Cheng and W. T. Fu, Strong efficiency in a locally convex space, Mathematical Methods of Operations Research, 50 (1999), 373-384.
doi: 10.1007/s001860050076. |
[6] |
H. W. Corley, Optimality conditions for maximizations of set-valued functions, Journal of Optimization Theory and Applications, 58 (1988), 1-10.
doi: 10.1007/BF00939767. |
[7] |
C. Gerth and P. Weidner, Nonconvex separation theorems and some applications in vector optimization, Journal of Optimization Theory and Applications, 67 (1990), 297-320.
doi: 10.1007/BF00940478. |
[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] |
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. |
[10] |
M. I. Henig, An improved definition of proper efficiency for vector maximization with respect to cones, Journal of Optimization Theory and Applications, 94 (1997), 469-486. |
[11] |
J. Jahn and R. Rauh, Contingent epiderivatives and set-valued optimzation, Mathematical Methods of Operation Research, 46 (1997), 193-211.
doi: 10.1007/BF01217690. |
[12] |
C. S. Lalitha, J. Dutta and M. G. Govll, Optimality criteria in set-valued optimization, ournal of the Australian mathematical society, 75 (2003), 221-231.
doi: 10.1017/S1446788700003736. |
[13] |
D. T. Luc., Contingent derivatives of set-valued maps and applications to vector optimization, Mathematical Programming, 50 (1991), 99-111.
doi: 10.1007/BF01594928. |
[14] |
X. Q. Yang, Directional derivatives for set-valued mappings and applications, Mathematical Methods of Operations Research, 48 (1998), 273-285.
doi: 10.1007/s001860050028. |
[15] |
Guolin Yu, Directional derivatives and generalized cone-preinvex set-valued optimizaiton, Acta Mathematica Sinica, Chinese Series (in Chinese), 54 (2011), 875-880. |
[16] |
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. |
[17] |
Guolin Yu and Sanyang Liu, Optimality conditions of globally proper efficient solutions for set-valued optimization problem, Acta Mathematicae Applicatae Sinica(in Chinese), 33 (2010), 150-160. |
[18] |
Guolin Yu, Henig globally efficiency for set-valued optimization and vector variational inequality, Journal of Systems Science & Complexity, 27 (2014), 338-349.
doi: 10.1007/s11424-014-1215-0. |
[19] |
Guolin Yu, Topological properties of Henig globally efficient solutions of set-valued optimization problems, Numerical Algebra, Control and Optimization, 4 (2014), 309-316.
doi: 10.3934/naco.2014.4.309. |
[20] |
X. Y. Zheng, Proper efficiency in locally convex topological vector spaces, Journal of Optimization Theory and Applications, 36 (1982), 387-407. |
show all references
References:
[1] |
M. Avriel and I. Zang , Generalized arcwise-connected functions and characterizations of local-global minimum properties, Journal of Optimization Theory and Applications, 32 (1980), 407-425.
doi: 10.1007/BF00934030. |
[2] |
J. Baier and J. Jahn, On subdifferentials of set-valued maps, Journal of Optimization Theory and Applications, 100 (1980), 233-240.
doi: 10.1023/A:1021733402240. |
[3] |
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. |
[4] |
J. M. Borwein and D. M. Zhuang, Super efficiency in vector optimiation, Transactions of the American Mathematical Society, 338 (1993), 105-122.
doi: 10.2307/2154446. |
[5] |
Y. H. Cheng and W. T. Fu, Strong efficiency in a locally convex space, Mathematical Methods of Operations Research, 50 (1999), 373-384.
doi: 10.1007/s001860050076. |
[6] |
H. W. Corley, Optimality conditions for maximizations of set-valued functions, Journal of Optimization Theory and Applications, 58 (1988), 1-10.
doi: 10.1007/BF00939767. |
[7] |
C. Gerth and P. Weidner, Nonconvex separation theorems and some applications in vector optimization, Journal of Optimization Theory and Applications, 67 (1990), 297-320.
doi: 10.1007/BF00940478. |
[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] |
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. |
[10] |
M. I. Henig, An improved definition of proper efficiency for vector maximization with respect to cones, Journal of Optimization Theory and Applications, 94 (1997), 469-486. |
[11] |
J. Jahn and R. Rauh, Contingent epiderivatives and set-valued optimzation, Mathematical Methods of Operation Research, 46 (1997), 193-211.
doi: 10.1007/BF01217690. |
[12] |
C. S. Lalitha, J. Dutta and M. G. Govll, Optimality criteria in set-valued optimization, ournal of the Australian mathematical society, 75 (2003), 221-231.
doi: 10.1017/S1446788700003736. |
[13] |
D. T. Luc., Contingent derivatives of set-valued maps and applications to vector optimization, Mathematical Programming, 50 (1991), 99-111.
doi: 10.1007/BF01594928. |
[14] |
X. Q. Yang, Directional derivatives for set-valued mappings and applications, Mathematical Methods of Operations Research, 48 (1998), 273-285.
doi: 10.1007/s001860050028. |
[15] |
Guolin Yu, Directional derivatives and generalized cone-preinvex set-valued optimizaiton, Acta Mathematica Sinica, Chinese Series (in Chinese), 54 (2011), 875-880. |
[16] |
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. |
[17] |
Guolin Yu and Sanyang Liu, Optimality conditions of globally proper efficient solutions for set-valued optimization problem, Acta Mathematicae Applicatae Sinica(in Chinese), 33 (2010), 150-160. |
[18] |
Guolin Yu, Henig globally efficiency for set-valued optimization and vector variational inequality, Journal of Systems Science & Complexity, 27 (2014), 338-349.
doi: 10.1007/s11424-014-1215-0. |
[19] |
Guolin Yu, Topological properties of Henig globally efficient solutions of set-valued optimization problems, Numerical Algebra, Control and Optimization, 4 (2014), 309-316.
doi: 10.3934/naco.2014.4.309. |
[20] |
X. Y. Zheng, Proper efficiency in locally convex topological vector spaces, Journal of Optimization Theory and Applications, 36 (1982), 387-407. |
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