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Well-posed constrained optimization problems in metric spaces

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Abstract

Relations between different notions of well-posedness of constrained optimization problems are studied. A characterization of the class of metric spaces in which Hadamard, strong, and Levitin-Polyak well-posedness of continuous minimization problems coincide is given. It is shown that the equivalence between the original Tikhonov well-posedness and the ones above provides a new characterization of the so-called Atsuji spaces. Generalized notions of well-posedness, not requiring uniqueness of the solution, are introduced and investigated in the above spirit.

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Authors and Affiliations

  1. Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    J. P. Revalski (Science Researcher) & N. V. Zhivkov (Science Researcher)

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  1. J. P. Revalski
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  2. N. V. Zhivkov
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Communicated by F. A. Potra

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Revalski, J.P., Zhivkov, N.V. Well-posed constrained optimization problems in metric spaces. J Optim Theory Appl 76, 145–163 (1993). https://doi.org/10.1007/BF00952826

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