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Saddle Points in Completely Regular Topological Spaces

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Abstract

We give a characterization of completely regular topological spaces. Applying some recent results for supinf problems in completely regular topological spaces we establish a variational principle for saddle points. Well-posedness of saddle point problems is studied as well.

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References

  1. Cavazzuti, E., Morgan, J.: Well-posed saddle point problems. In: Hiriart-Urruty, J.-B., Oettli, W., Stoer, J. (eds.) Optimization: Theory and Algorithms. Proc. Conf. Confolant (France 1981). Lecture Notes in Pure and Appl. Math., vol. 86, pp. 61–76. Marcel Dekker Inc., New York (1983)

  2. Cullen, H.F.: Introduction to General Topology. Heath, Boston (1967)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. Gaumont, D., Kamburova, D., Revalski, J.P.: Perturbations of supinf problems with constraints. Vietnam J. Math. 47, 659–667 (2019)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  9. Oettli, W., Théra, M.: Equivalents of Ekeland’s principle. Bull. Aust. Math. Soc. 48, 385–392 (1993)

    Article  MathSciNet  Google Scholar 

  10. Sullivan, F.: A characterization of complete metric spaces. Proc. Amer. Math. Soc. 83, 345–346 (1981)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors extend their heartfelt thanks to Prof. Petar Kenderov, who proposed the idea of considering variational principles for saddle point problems in completely regular topological spaces. Additionally, they highly appreciate his ongoing support and encouragement. The research of D. Kamburova and N. Zlateva is financed by the European Union-NextGenerationEU, through the National Recovery and Resilience Plan of the Republic of Bulgaria, project SUMMIT BG-RRP-2.004-0008-C01.

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Authors and Affiliations

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

    Detelina Kamburova

  2. Department of Mathematics and Physics, Technical University of Varna, 1, Studentska Str., 9010, Varna, Bulgaria

    Rumen Marinov

  3. Faculty of Mathematics and Informatics, Sofia University, 5, James Bourchier Blvd., 1164, Sofia, Bulgaria

    Nadia Zlateva

Authors
  1. Detelina Kamburova
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  2. Rumen Marinov
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  3. Nadia Zlateva
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The second and third authors contributed equally to this work.

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Correspondence to Nadia Zlateva.

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Kamburova, D., Marinov, R. & Zlateva, N. Saddle Points in Completely Regular Topological Spaces. Vietnam J. Math. (2024). https://doi.org/10.1007/s10013-024-00689-9

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  • DOI: https://doi.org/10.1007/s10013-024-00689-9

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