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Well-posed constrained optimization problems in metric spaces. (English) Zbl 0798.49031
Summary: 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.

MSC:
49K35 Optimality conditions for minimax problems
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