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Global proper efficiency and vector optimization with conearcwise connected setvalued maps
1.  Institute of Applied Mathematics, Beifang University of Nationalities, Yinchuan 750021 
References:
[1] 
M. Avriel and I. Zang , Generalized arcwiseconnected functions and characterizations of localglobal minimum properties, Journal of Optimization Theory and Applications, 32 (1980), 407425. doi: 10.1007/BF00934030. 
[2] 
J. Baier and J. Jahn, On subdifferentials of setvalued maps, Journal of Optimization Theory and Applications, 100 (1980), 233240. 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), 232241. doi: 10.1016/0022247X(79)902269. 
[4] 
J. M. Borwein and D. M. Zhuang, Super efficiency in vector optimiation, Transactions of the American Mathematical Society, 338 (1993), 105122. 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), 373384. doi: 10.1007/s001860050076. 
[6] 
H. W. Corley, Optimality conditions for maximizations of setvalued functions, Journal of Optimization Theory and Applications, 58 (1988), 110. 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), 297320. doi: 10.1007/BF00940478. 
[8] 
X. H. Gong, H. B. Dong and S. Y. Wang, Optimality conditions for proper efficient solutions of vector setvalued optimization, Journal of Mathematical Analysis and Applications, 284 (2003), 332350. doi: 10.1016/S0022247X(03)003603. 
[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), 1231. 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), 469486. 
[11] 
J. Jahn and R. Rauh, Contingent epiderivatives and setvalued optimzation, Mathematical Methods of Operation Research, 46 (1997), 193211. doi: 10.1007/BF01217690. 
[12] 
C. S. Lalitha, J. Dutta and M. G. Govll, Optimality criteria in setvalued optimization, ournal of the Australian mathematical society, 75 (2003), 221231. doi: 10.1017/S1446788700003736. 
[13] 
D. T. Luc., Contingent derivatives of setvalued maps and applications to vector optimization, Mathematical Programming, 50 (1991), 99111. doi: 10.1007/BF01594928. 
[14] 
X. Q. Yang, Directional derivatives for setvalued mappings and applications, Mathematical Methods of Operations Research, 48 (1998), 273285. doi: 10.1007/s001860050028. 
[15] 
Guolin Yu, Directional derivatives and generalized conepreinvex setvalued optimizaiton, Acta Mathematica Sinica, Chinese Series (in Chinese), 54 (2011), 875880. 
[16] 
Guolin Yu and Sanyang Liu, Globally proper saddle point in icconeconvexlike setvalued optimization problems, Act Mathematica Sinica (English Series), 25 (2009), 19211928. doi: 10.1007/s1011400961449. 
[17] 
Guolin Yu and Sanyang Liu, Optimality conditions of globally proper efficient solutions for setvalued optimization problem, Acta Mathematicae Applicatae Sinica(in Chinese), 33 (2010), 150160. 
[18] 
Guolin Yu, Henig globally efficiency for setvalued optimization and vector variational inequality, Journal of Systems Science & Complexity, 27 (2014), 338349. doi: 10.1007/s1142401412150. 
[19] 
Guolin Yu, Topological properties of Henig globally efficient solutions of setvalued optimization problems, Numerical Algebra, Control and Optimization, 4 (2014), 309316. 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), 387407. 
show all references
References:
[1] 
M. Avriel and I. Zang , Generalized arcwiseconnected functions and characterizations of localglobal minimum properties, Journal of Optimization Theory and Applications, 32 (1980), 407425. doi: 10.1007/BF00934030. 
[2] 
J. Baier and J. Jahn, On subdifferentials of setvalued maps, Journal of Optimization Theory and Applications, 100 (1980), 233240. 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), 232241. doi: 10.1016/0022247X(79)902269. 
[4] 
J. M. Borwein and D. M. Zhuang, Super efficiency in vector optimiation, Transactions of the American Mathematical Society, 338 (1993), 105122. 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), 373384. doi: 10.1007/s001860050076. 
[6] 
H. W. Corley, Optimality conditions for maximizations of setvalued functions, Journal of Optimization Theory and Applications, 58 (1988), 110. 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), 297320. doi: 10.1007/BF00940478. 
[8] 
X. H. Gong, H. B. Dong and S. Y. Wang, Optimality conditions for proper efficient solutions of vector setvalued optimization, Journal of Mathematical Analysis and Applications, 284 (2003), 332350. doi: 10.1016/S0022247X(03)003603. 
[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), 1231. 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), 469486. 
[11] 
J. Jahn and R. Rauh, Contingent epiderivatives and setvalued optimzation, Mathematical Methods of Operation Research, 46 (1997), 193211. doi: 10.1007/BF01217690. 
[12] 
C. S. Lalitha, J. Dutta and M. G. Govll, Optimality criteria in setvalued optimization, ournal of the Australian mathematical society, 75 (2003), 221231. doi: 10.1017/S1446788700003736. 
[13] 
D. T. Luc., Contingent derivatives of setvalued maps and applications to vector optimization, Mathematical Programming, 50 (1991), 99111. doi: 10.1007/BF01594928. 
[14] 
X. Q. Yang, Directional derivatives for setvalued mappings and applications, Mathematical Methods of Operations Research, 48 (1998), 273285. doi: 10.1007/s001860050028. 
[15] 
Guolin Yu, Directional derivatives and generalized conepreinvex setvalued optimizaiton, Acta Mathematica Sinica, Chinese Series (in Chinese), 54 (2011), 875880. 
[16] 
Guolin Yu and Sanyang Liu, Globally proper saddle point in icconeconvexlike setvalued optimization problems, Act Mathematica Sinica (English Series), 25 (2009), 19211928. doi: 10.1007/s1011400961449. 
[17] 
Guolin Yu and Sanyang Liu, Optimality conditions of globally proper efficient solutions for setvalued optimization problem, Acta Mathematicae Applicatae Sinica(in Chinese), 33 (2010), 150160. 
[18] 
Guolin Yu, Henig globally efficiency for setvalued optimization and vector variational inequality, Journal of Systems Science & Complexity, 27 (2014), 338349. doi: 10.1007/s1142401412150. 
[19] 
Guolin Yu, Topological properties of Henig globally efficient solutions of setvalued optimization problems, Numerical Algebra, Control and Optimization, 4 (2014), 309316. 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), 387407. 
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