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广义向量混合变分不等式的Levitin-Polyak适定性

, PP. 655-662

Keywords: Levitin-Polyak-适定性,广义向量混合变分不等式,标量函数,gap函数,优化问题

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Abstract:

首先给出了广义向量混合变分不等式的Levitin-Polyak-近似序列以及适定性的概念.然后,定义了广义向量混合变分不等式的gap函数,并证明了广义向量混合变分不等式的Levitin-Polyak-适定性与其相应的gap函数所定义的优化问题的Levitin-Polyak-适定性之间的等价关系.最后,研究了广义向量混合变分不等式的Levitin-Polyak-适定性的Furi-Vignoli型度量性质.

References

[1]  Margiocc M, Patrone F, Chicco L P, et al. Metric characterizations of Tykhonov well-posedness in value[J]. J Optim Theory Appl,1999,100(2):377-387.
[2]  Hu R, Fang Y P. Levitin-Polyak well-posedness variational inequalities[J]. Nonlinear Anal,2010,72:373-381.
[3]  Huang X X, Yang X Q. Generalized Levitin-Polyak well-posedness in constrained optimization[J]. SIAM J Optim,2006,17(1):243-258. [4] Morgan J. Approximations and well-posedness in multicriteria game[J]. Ann Oper Res,2005,137(1):257-268.
[4]  Lucchetti R, Patrone F. A characterization of Tykhonov well-posedness for minimum problems with applications to variational inequalities[J]. Numer Funct Anal Optim,1981,3(4):461-476.
[5]  Lignola M B. Well-posedness and L-well-poseness for quasivariational inequalities[J]. J Optim Theory Appl,2006,128(1):119-138.
[6]  Fang Y P, Huang N J, Yao J C. Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems[J]. J Glob Optim,2008,41:117-133.
[7]  Giannessi F. Theorem of Alternative, Ratic Programs, and Complementarity Problems[C]//Cottle R W, Giannessi F, Lions J L. Variational Inequalities and Complementarity Problems. Chichester:Wiley,1980:151-186.
[8]  夏福全,黎小波. Banach空间中分离变分不等式的Levitin-Polyak-α适定性[J]. 四川师范大学学报:自然科学版,2012,35(3):430-434.
[9]  Huang X X. Extended and strongly extendedwell-posedness of set-valued optimization problems[J]. Math Meth Oper Res,2001,53:101-116.
[10]  Li S J, Li M H. Levitin-Polyak well-posedness of vector equilibrium problems[J]. Math Meth Oper Res,2009,69:125-140.
[11]  Zhang S S. Variational Inequality and Its Related Problems in Chinese[M]. Chongqing:Chongqing Press,2008.
[12]  Nadler S B. Multi-valued contraction mapping[J]. Pacific J Math,1969,30:475-488.
[13]  Chen G Y, Yang X Q, Yu H. A nonlinear scalarization function and generalized quasi-vector equilibrium problems[J]. J Glob Optim,2005,32:451-466.
[14]  Lignola M B, Morgan J. α-well-posedness for Nash equilibria and for optimization problems with Nash equilibrium constraints[J]. J Glob Optim,2006,36:439-459.
[15]  Kuratowski K. Topology[M]. New York:Academia Press,1968.

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