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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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