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Well-posed constrained optimization problems in metric spaces (1993)

Revalski, J. P. ; Zhivkov, N. V.

Springer

Journal of optimization theory and applications 76 (1993), S. 145-163

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ISSN: 1573-2878

Keywords: Optimization problems ; well-posedness ; stability

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00952826

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