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Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification
Kybernetika, Tome 49 (2013) no. 3, pp. 446-464 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian-Fromovitz Constraint Qualification, we establish relationships between tilt stability and some other stability notions in constrained optimization. Involving further the well-known Constant Rank Constraint Qualification, we derive new necessary and sufficient conditions for tilt-stable local minimizers.
The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian-Fromovitz Constraint Qualification, we establish relationships between tilt stability and some other stability notions in constrained optimization. Involving further the well-known Constant Rank Constraint Qualification, we derive new necessary and sufficient conditions for tilt-stable local minimizers.
Classification : 49J52, 90C30, 90C31
Keywords: variational analysis; second-order theory; generalized differentiation; tilt stability 
@article{KYB_2013_49_3_a5,
     author = {Mordukhovich, Boris S. and Outrata, Ji\v{r}{\'\i} V.},
     title = {Tilt stability in nonlinear programming under {Mangasarian-Fromovitz} constraint qualification},
     journal = {Kybernetika},
     pages = {446--464},
     year = {2013},
     volume = {49},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013_49_3_a5/}
}
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Mordukhovich, Boris S.; Outrata, Jiří V. Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification. Kybernetika, Tome 49 (2013) no. 3, pp. 446-464. http://geodesic.mathdoc.fr/item/KYB_2013_49_3_a5/