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July  2015, 11(3): 701-714. doi: 10.3934/jimo.2015.11.701

Levitin-Polyak well-posedness of a system of generalized vector variational inequality problems

Jian-Wen Peng 1, and  Xin-Min Yang 1,

1. 

School of Mathematics, Chongqing Normal University, Chongqing 400047, China, China

Received  February 2012 Revised  May 2014 Published  October 2014

In this paper, we introduce two types of Levitin-Polyak well-posedness for a system of generalized vector variational inequality problems. By means of a gap function of the system of generalized vector variational inequality problems, we establish equivalence between the two types of Levitin-Polyak well-posedness of the system of generalized vector variational inequality problems and the corresponding well-posednesses of the minimization problems. We also present some metric characterizations for the two types of Levitin-Polyak well-posedness of the system of generalized vector variational inequality problems. The results in this paper generalize, extend and improve some known results in the literature.
Keywords: metric characterization., Levitin-Polyak approximating solution sequence, Levitin-Polyak well-posedness, System of generalized vector variational inequality problems, gap function.
Mathematics Subject Classification: Primary: 49K40, 90C31; Secondary: 47J2.
Citation: Jian-Wen Peng, Xin-Min Yang. Levitin-Polyak well-posedness of a system of generalized vector variational inequality problems. Journal of Industrial & Management Optimization, 2015, 11 (3) : 701-714. doi: 10.3934/jimo.2015.11.701
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show all references

References:
[1]

J. Optim. Theory and Appl., 107 (2000), 547-557. doi: 10.1023/A:1026495115191.  Google Scholar

[2]

Bull. Austr. Math. Soc., 59 (1999), 433-442. doi: 10.1017/S0004972700033116.  Google Scholar

[3]

John Wiley & Sons, 1984.  Google Scholar

[4]

in Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 294 (1987), 51-61. doi: 10.1007/978-3-642-46618-2_2.  Google Scholar

[5]

Report 6, Istituto di econometria e Matematica per le decisioni economiche, Universita Cattolica del Sacro Cuore, Milan, Italy, 1993. Google Scholar

[6]

Nonlinear Analysis, TMA, 69 (2008), 4585-4603. doi: 10.1016/j.na.2007.11.015.  Google Scholar

[7]

Lecture notes in economics and mathematical systems. Springer, Berlin 2005.  Google Scholar

[8]

J. Optim. Theory and Appl., 59 (1988), 369-390. doi: 10.1007/BF00940305.  Google Scholar

[9]

J. Optim. Theory and Appl., 132 (2007), 213-226. doi: 10.1007/s10957-006-9144-2.  Google Scholar

[10]

J. Optim. Theory and Appl., 141 (2009), 285-297. doi: 10.1007/s10957-008-9494-z.  Google Scholar

[11]

RAIRO Oper. Res., 37 (2003), 195-208. doi: 10.1051/ro:2003021.  Google Scholar

[12]

Springer-Verlag , 1993.  Google Scholar

[13]

In variational inequalities and complementarity problems, (Edited by R. W. Cottle, F. Giannessi, and J. L. Lions), John Wiley and Sins, New york, (1980), 151-186.  Google Scholar

[14]

Computers and Mathematics with Applications, 53 (2007), 1306-1316. doi: 10.1016/j.camwa.2006.09.009.  Google Scholar

[15]

J. Glob. Optim., 41 (2008), 117-133. doi: 10.1007/s10898-007-9169-6.  Google Scholar

[16]

J. Optim. Theory Appl., 5 (1970), 223-229. \vspace*{2pt}  Google Scholar

[17]

Nonlinear Analysis, TMA, 72 (2010), 373-381. doi: 10.1016/j.na.2009.06.071.  Google Scholar

[18]

J. Optim. Theory and Appl., 106 (2000), 165-182. doi: 10.1023/A:1004615325743.  Google Scholar

[19]

Math. Meth. Oper. Res., 53 (2001), 101-116. doi: 10.1007/s001860000100.  Google Scholar

[20]

SIAM J. Optim., 17 (2006), 243-258. doi: 10.1137/040614943.  Google Scholar

[21]

J. Glob. Optim., 37 (2007), 287-304. doi: 10.1007/s10898-006-9050-z.  Google Scholar

[22]

Numer. Funct. Anal. Optim., 31 (2010), 440-459. doi: 10.1080/01630563.2010.485296.  Google Scholar

[23]

J. Ind. Manag. Optim., 3 (2007), 671-684. doi: 10.3934/jimo.2007.3.671.  Google Scholar

[24]

J. Glob. Optim., 44 (2009), 159-174. doi: 10.1007/s10898-008-9310-1.  Google Scholar

[25]

Numer. Funct. Anal. Optim., 15 (1994), 889-907. doi: 10.1080/01630569408816598.  Google Scholar

[26]

Warszawa, Poland, 1952. Google Scholar

[27]

Numer. Funct. Anal. Optim., 30 (2009), 548-565. doi: 10.1080/01630560902987972.  Google Scholar

[28]

Soviet Mathematics Doklady, 7 (1966), 764-767. Google Scholar

[29]

J. Ind. Manag. Optim., 5 (2009), 683-696. doi: 10.3934/jimo.2009.5.683.  Google Scholar

[30]

in Decision and Control in Management Science, Kluwer Academic Publishers, 4 (2002), 367-377. doi: 10.1007/978-1-4757-3561-1_20.  Google Scholar

[31]

Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, 331 (1995), 171-192.  Google Scholar

[32]

Springer, Berlin, 1989.  Google Scholar

[33]

Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 294 (1987), 194-207. doi: 10.1007/978-3-642-46618-2_13.  Google Scholar

[34]

springer, 2006.  Google Scholar

[35]

Numer. Funct. Anal. Optim., 3 (1981), 461-476. doi: 10.1080/01630568108816100.  Google Scholar

[36]

Mathematical Programming, 31 (1985), 206-219. doi: 10.1007/BF02591749.  Google Scholar

[37]

USSRJ. Comput. Math. Math. Phys., 6 (1966), 28-33. doi: 10.1016/0041-5553(66)90003-6.  Google Scholar

[38]

Math. Meth. Oper. Res., 67 (2008), 505-524. doi: 10.1007/s00186-007-0200-y.  Google Scholar

[39]

J. Optim. Theory Appl., 91 (1996), 257-266. doi: 10.1007/BF02192292.  Google Scholar

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