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Equilibrium and least element problems for multivalued functions

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Abstract

The principal aim of this paper is to extend some recent results which concern problems involving bifunctions to similar generalized problems for multivalued bifunctions. To this end, by using the appropriate notions of strict pseudomonotonicity we establish the relationships between generalized vector equilibrium problems and generalized minimal element problems of feasible sets. Moreover relationships between generalized least element problems of feasible sets and generalized vector equilibrium problems are studied by employing the concept of Z-multibifunctions.

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References

  1. Ansari Q.H., Lai T.C., Yao J.C.: On the equivalence of extended generalized complementarity problems and generalized least element problems. J. Optim. Theory Appl. 102(2), 277–288 (1999)

    Article  Google Scholar 

  2. Chen G.Y., Li S.J.: Existence of solutions for generalized vector quasivariational inequalities. J. Optim. Theory Appl. 90(2), 321–334 (1996)

    Article  Google Scholar 

  3. Cryer C.W., Dempster M.A.H.: Equivalence of linear complementarity problems and linear programs in vector lattice hilbert spaces. SIAM. J. Control Optim. 18(1), 76–90 (1980)

    Article  Google Scholar 

  4. Fang Y.-P., Huang N.-J.: Equivalence of equilibrium problems and least-element problems. J. Optim. Theory Appl. 132, 411–422 (2007)

    Article  Google Scholar 

  5. Fang Y.-P., Huang N.-J.: Vector equilibrium problems, minimal elements problems and least element problems. Positivity 11, 251–268 (2007)

    Article  Google Scholar 

  6. Konnov I.V., Yao J.C.: Existence of solutions for generalized vector equilibrium problems. J. Math. Anal. Appl. 233, 328–335 (1999)

    Article  Google Scholar 

  7. Riddell R.C.: Equivalence of nonlinear complementarity problems and least element problems in Banach lattices. Math. Oper. Res. 6(3), 462–474 (1981)

    Article  Google Scholar 

  8. Schaible S., Yao J.C.: On the equivalence of nonlinear complementarity problems and least-element problems. Math. Program. 70, 191–200 (1995)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Quantitative Methods, Brescia University, Contrada S.Chiara, 50, Brescia, Italy

    E. Allevi

  2. Department of Mathematics, Statistics, Informatics and Applications, Bergamo University, Piazza Rosate, 2, Bergamo, 24129, Italy

    A. Gnudi

  3. Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, 32023, Taiwan

    S. Schaible

  4. Department of Information Engineering and Mathematical Models, Bergamo University, viale Marconi 5, Dalmine, 24044, Italy

    M. T. Vespucci

Authors
  1. E. Allevi
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  2. A. Gnudi
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  3. S. Schaible
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  4. M. T. Vespucci
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Correspondence to S. Schaible.

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Allevi, E., Gnudi, A., Schaible, S. et al. Equilibrium and least element problems for multivalued functions. J Glob Optim 46, 561–569 (2010). https://doi.org/10.1007/s10898-009-9440-0

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  • DOI: https://doi.org/10.1007/s10898-009-9440-0

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