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Levitin–Polyak well-posedness in generalized vector variational inequality problem with functional constraints

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Abstract

In this paper, we study Levitin–Polyak type well-posedness for generalized vector variational inequality problems with abstract and functional constraints. Various criteria and characterizations for these types of well-posednesses are given.

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References

  • Auslender A (2003) Variational inequalities over the cone of semidefinite positive symmetric matrices and over the Lorentz cone, the second japanese-sino optimization meeting, part ii, kyoto, 2002. Optim Methods Softw 18: 359–376

    Article  MATH  MathSciNet  Google Scholar 

  • Beer G, Lucchetti R (1992) The epi-distance topology: continuity and stability results with application to convex optimization problems. Math Oper Res 17: 715–726

    Article  MATH  MathSciNet  Google Scholar 

  • Chen GY, Huang XX, Yang XQ (2005) Vector optimization, set-valued and variational analysis. Lecture notes in economics and mathematical systems. Springer, Berlin

    Google Scholar 

  • Chen GY, Yen ND (1993) On the variational inequality model for network equilibrium, Internet Report, Department of Mathematics, University of Pisa, 3.196 (724)

  • Dontchev AL, Zolezzi T (1993) Well-posed optimization problems. Lecture notes in mathematics, vol 1543. Springer, Berlin

    Google Scholar 

  • Furi M, Vignoli A (1970) About well-posed minimization problems for functionals in metric spaces. J Optim Theor Appl 5: 225–229

    Article  MATH  Google Scholar 

  • Giannessi F (1980) Theorems of alternative, quadratic programs and complementarity problems. In: Cottle RW, Giannessi F, Lions JL (eds) Variational inequality and complementarity problems. Wiley, New York

    Google Scholar 

  • Huang XX, Yang XQ (2006) Generalized Levitin–Polyak well-posedness in constraints optimization. SIAM J Optim 17: 243–258

    Article  MATH  MathSciNet  Google Scholar 

  • Huang XX, Yang XQ (2007a) Levitin–Polyak well-Posedness of constrained vector optimization problems. J Glob Optim 37: 287–304

    Article  MATH  MathSciNet  Google Scholar 

  • Huang XX, Yang XQ (2007b) Levitin–Polyak well-posedness in generalized variational inequality problems with functional constraints. J Ind Management Optim 3: 671–684

    MATH  MathSciNet  Google Scholar 

  • Huang XX, Yang XQ (2007c) Characterizations of the nonemptiness and compactness of the solution set of a vector variational inequality problem and applications (submitted for publication)

  • Huang XX, Yang XQ (2007d) Levitin–Polyak well-posedness of vector variational inequality problems with functional constraints (submitted for publication)

  • Huang XX, Yang XQ, Zhu DL (2007) Levitin–Polyak well-posedness of variational inequality problems with functional constraints (submitted for publication)

  • Konsulova AS, Revalski JP (1994) Constrained convex optimization problems well-posedness and stability. Numer Funct Anal Optim 15: 889–907

    Article  MATH  MathSciNet  Google Scholar 

  • Levitin ES, Polyak BT (1966) Convergence of minimizing sequences in conditional extremum problems. Soviet Math Dokl 7: 764–767

    MATH  Google Scholar 

  • Luc DT (1989) Theory of vector optimization. Springer, Berlin

    Google Scholar 

  • Lucchetti R, Revalski I (eds) (1995) Recent development in well-posed variational problems. Kluwer, Dordrecht

    Google Scholar 

  • Revalski JP (1997) Hadamard and strong well-posedness for convex programs. SIAM J Optim 7: 519–526

    Article  MATH  MathSciNet  Google Scholar 

  • Tykhonov AN (1966) On the stability of the functional optimization problem. USSR Compt Math Math Phys 6: 28–33

    Article  Google Scholar 

  • Yang XQ (1993) Vector variational inequalities and its duality. Nonlinear Anal TMA 21: 867–877

    Article  Google Scholar 

  • Zolezzi T (1996) Extended well-posedness of optimization problems. J Optim Theo Appl 91: 257–266

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to X. X. Huang.

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This research is partially supported by the National Science Foundation of China and Shanghai Pujiang Program.

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Xu, Z., Zhu, D.L. & Huang, X.X. Levitin–Polyak well-posedness in generalized vector variational inequality problem with functional constraints. Math Meth Oper Res 67, 505–524 (2008). https://doi.org/10.1007/s00186-007-0200-y

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