Well-posed constrained optimization problems in metric spaces |
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Authors: | J P Revalski N V Zhivkov |
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Institution: | (1) Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria |
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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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Keywords: | Optimization problems well-posedness stability |
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