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Perturbations of Supinf Problems with Constraints

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Abstract

We investigate constrained supinf problems for functions of two variables. Conditions are given which assure that the objective function can be perturbed by continuous functions with arbitrary small norms in such a way that the supinf problem for the perturbed function has a solution. We also give a characterization of the notion of well-posedness for such problems.

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References

  1. Ekeland, I.: On the variational principle. J. Math. Anal. Appl. 47, 324–353 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ioffe, A.D., Lucchetti, R.E., Revalski, J.P.: A variational principle for problems with functional constraints. SIAM J. Optim. 12, 461–478 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Kenderov, P.S., Lucchetti, R.E.: Generic well-posedness of supinf problems. Bull. Austr. Math. Soc. 54, 5–25 (1996)

    Article  MATH  Google Scholar 

  4. Kenderov, P.S., Revalski, J.P.: Dense existence of solutions of perturbed optimization problems and topological games. C. R. Acad. Bulg. Sci. 63, 937–942 (2010)

    MathSciNet  MATH  Google Scholar 

  5. Kenderov, P., Revalski, J.P.: Variational principles for supinf problems. C. R. Acad. Bulg. Sci. 70, 1635–1642 (2017)

    MathSciNet  MATH  Google Scholar 

  6. Loridan, P., Morgan, J.: New results on approximate solution in two-level optimization. Optimization 20, 819–836 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  7. Loridan, P., Morgan, J.: Weak via strong Stackelberg problem: New results. J. Glob. Optim. 8, 263–287 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. McLinden, L.: An application of Ekeland’s theorem to minmax problems. Nonlinear Anal. TMA 6, 189–196 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  9. von Stackelberg, H.: Market Structure and Equilibrium. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

Download references

Acknowledgements

The second author has been partially supported by the Bulgarian National Fund for Scientific Research, under grant KP-06-H22/4.

The third author has been partially supported by the Bulgarian National Fund for Scientific Research, under grant DFNI-DNTS/Russia 01/9/2017.

Part of the results in this article were obtained while the third author was visiting professor during the second semester of 2018 at the Pantheon-Assas University, Paris.

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Authors and Affiliations

  1. CRED EA 7321, Université Panthéon-Assas, 12, place du Panthéon, 75231, Paris Cedex 05, France

    D. Gaumont

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., block 8, 1113, Sofia, Bulgaria

    D. Kamburova & J. P. Revalski

Authors
  1. D. Gaumont
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  2. D. Kamburova
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  3. J. P. Revalski
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Correspondence to J. P. Revalski.

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Dedicated to the 80th birthday of Alexander Ioffe.

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Gaumont, D., Kamburova, D. & Revalski, J.P. Perturbations of Supinf Problems with Constraints. Vietnam J. Math. 47, 659–667 (2019). https://doi.org/10.1007/s10013-019-00351-9

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  • DOI: https://doi.org/10.1007/s10013-019-00351-9

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