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Local wellposedness of constrained problems. (English) Zbl 0867.49020
Summary: A notion of local wellposedness for constrained problems requires existence and uniqueness of the local minimizer \(x_0\) in a neighborhood of an arbitrary point \(x^*\) and strong convergence of every locally asymptotically minimizing sequence to \(x_0\). Local wellposedness is shown to be intimately related to the differentiability properties of the value function. Results of T. Zolezzi [Nonlinear Anal., Theory Methods Appl. 25, No. 5, 437-453 (1995; Zbl 0841.49005); “Buona posizione dei problemi vincolati”, Dip. Mat. Univ. Genova (1994), per bibl.] for global constrained problems are thereby extended and examples about mathematical programming are presented.

MSC:
49K40 Sensitivity, stability, well-posedness
90C31 Sensitivity, stability, parametric optimization
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References:
[1] Dontchev A., Lecture Notes in Mathematics
[2] DOI: 10.1090/S0273-0979-1979-14595-6 · Zbl 0441.49011
[3] DOI: 10.1287/moor.4.4.458 · Zbl 0433.90075
[4] DOI: 10.1016/0041-5553(66)90003-6 · Zbl 0212.23803
[5] Zolezzi T., Nonlinear Anal. Theory Methods Appl (1995)
[6] Zolezzi T., Buona posizione dei problemi vincolati
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