Articles

LEVITIN-POYAK WELL-POSEDNESS OF EQUILIBRIUM PROBLEMS GENERALIZED VECTOR WITH FUNCTIONAL CONSTRAINTS

  • WANG Gang ,
  • HUANG Xue-Xiang ,
  • ZHANG Jie ,
  • CHEN Guang-Ya
Expand

Received date: 2009-01-07

  Online published: 2010-09-20

Supported by

This work is supported by the National Science Foundation of China and Shanghai Pujian Program

Abstract

In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given.

Cite this article

WANG Gang , HUANG Xue-Xiang , ZHANG Jie , CHEN Guang-Ya . LEVITIN-POYAK WELL-POSEDNESS OF EQUILIBRIUM PROBLEMS GENERALIZED VECTOR WITH FUNCTIONAL CONSTRAINTS[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1400 -1412 . DOI: 10.1016/S0252-9602(10)60132-4

References

[1] Chen G Y, Huang X X, Yang X Q. Vecotr Optimization, Set-Valued and Variational Analysis. Berlin: Springer-Verlag, 2005

[2] Chiang Y, Chadli O, Yao J C. Generalized vector equilibrium problems with trifunctions. J Global Optim, 2004, 30: 135--154

[3] Flores B F. Existence theorems for generalized noncoercive equilibrium problems: the quasiconvex case. SIAM J Optim, 2000, 11: 675--690

[4] Fang Y P, Hu R, Huang N J. Well-posedness for equilibrium problems and for optimization problems with equilibrium constraints Programming. Comput Math Appl, 2008, 50: 89--100

[5] Huang L G. The solution sets and connectedness for weak vector variational inequalities. Acta Mathematica Scientia, 2009, 29A(1): 114--120

[6] Huang X X, Teo K L, Yang X Q. Calmness and exact penalization in vector optimization with cone constraints. Comput Optim Appl, 2006, 35: 47--67
 
[7] Huang X X, Yang X Q. Generalized Levitin-Polyak well-posedness in constrained optimization. SIAM J Optim, 2006, 17: 243--258

[8] Huang X X, Yang X Q. Levitin-Polyak well-posedness of constrained vector optimization problems. J Glob Optim, 2007, 37: 287--304

[9] Huang X X, Yang X Q. Levitin-Polyak well-posedness in generalized variational inequality problemes with functional constraints. J Ind Manag Optim, 2007, 3: 671--684

[10] Kuratowski K. Topology Part I and Part II. New York: Academic Press, 1968

[11] Levitin E S, Polyak B T. Convergence of minimizing sequences in conditional extremum problems. Soviet Math Dokl, 1966, 7: 764--767

[12] Li S J, Teo K L, Yang X Q. Gap function and existence of solutions to generlized vector quasi-equilibrium problems. J Glob Optim, 2006, 34: 427--440

[13] Li S J, Li M H. Levitin-Polyak well-posedness of vector equilibrium problems. Math Methods Oper Res, accepted

[14] Tykhonov A N. On the stability of the functional optimization problem. USSR Compt Math Math Phys, 1966, 6: 28--33

[15] Xu Z, Zhu D L, Huang X X. Levitin-Polyak well-posedness in generalized vector variational inequality problems with functional constraints. Math Methods Oper Res, 2008, 67: 505--524

Outlines

/