Kybernetika 49 no. 3, 446-464, 2013

Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification

This article was granted Editor's award of the year 2013Editor's award 2013

Boris S. Mordukhovich and Jiří V. Outrata


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.


variational analysis, second-order theory, generalized differentiation, tilt stability


49J52, 90C30, 90C31


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