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A Scalarization Approach for Vector Variational Inequalities with Applications

This paper is dedicated to Professor Franco Giannessi for his 68th birthday

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Abstract

We consider an approach to convert vector variational inequalities into an equivalent scalar variational inequality problem with a set-valued cost mapping. Being based on this property, we give an equivalence result between weak and strong solutions of set-valued vector variational inequalities and suggest a new gap function for vector variational inequalities. Additional examples of applications in vector optimization, vector network equilibrium and vector migration equilibrium problems are also given

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References

  1. Q.H. Ansari I.V. Konnov J.-C. Yao (2001) ArticleTitleExistence of a solution and variational principles for vector equilibrium problems J. Optimization Theory and Applications 110 481–492 Occurrence Handle10.1023/A:1017581009670

    Article  Google Scholar 

  2. J.-P. Aubin (1993) Optima and Equilibria: An Introduction to Nonlinear Analysis Springer-Verlag Berlin-Heidelberg-New York

    Google Scholar 

  3. Chen G.-Y., Goh C.J., Yang X.Q. (2000). On gap functions for vector variational inequalities, in [4], 55–72.

  4. F Giannessi (Eds) (1999) Vector Variational Inequalities and Vector Equilibria Mathematical Theories. Kluwer Academic Publishers Dordrecht

    Google Scholar 

  5. C.J. Goh X.Q. Yang (1999) ArticleTitleVector equilibrium problem and vector optimization European J. Operations Research 116 615–628 Occurrence Handle10.1016/S0377-2217(98)00047-2

    Article  Google Scholar 

  6. N. Hadjisavvas S. Schaible (1998) Quasimonotonicity and pseudomonotonicity in variational inequalities and equilibrium problems J.-P. Crouzeix J.-E. Martinez-Legaz M Volle (Eds) Generalized Convexity, Generalized Monotonicity. Kluwer Academic Publishers Dordrecht 257–275

    Google Scholar 

  7. H. Kneser (1952) ArticleTitleSur le théorème fondamentale de la otheorie des jeux C.R. Acad. Sci. Paris 234 2418–2420

    Google Scholar 

  8. I.V. Konnov (2001) On vector equilibrium and vector variational inequality problems N. Hadjisavvas J.-E. Martinez-Legaz J.-P Penot (Eds) Generalized Convexity and Generalized Monotonicity. Springer-Verlag Berlin-Heidelberg-New York 247–263

    Google Scholar 

  9. D.T. Luc (1989) Theory of Vector Optimization Springer-Verlag Berlin-Heidelberg-New York

    Google Scholar 

  10. A. Nagurney (1993) Network Economics: A Variational Inequality Approach Kluwer Academic Publishers Dordrecht

    Google Scholar 

  11. V.V. Podinovskii V.D. Nogin (1982) Pareto-Optimal Solutions of Multicriteria Problems Nauka Moscow

    Google Scholar 

  12. X.Q. Yang C.J. Goh (1997) ArticleTitleOn vector variational inequalities: application to vector equilibria J. Optimization Theory and Applications 95 431–443 Occurrence Handle10.1023/A:1022647607947

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Kazan University ul.Kremlevskaya, Kazan, 18,420008, Russia

    Igor V. Konnov

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  1. Igor V. Konnov
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Correspondence to Igor V. Konnov.

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Mathematics Subject Classification(2000). 49J40, 65K10, 90C29

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Konnov, I.V. A Scalarization Approach for Vector Variational Inequalities with Applications. J Glob Optim 32, 517–527 (2005). https://doi.org/10.1007/s10898-003-2688-x

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  • DOI: https://doi.org/10.1007/s10898-003-2688-x

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