Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification

Boris S. Mordukhovich; Jiří V. Outrata

Kybernetika (2013)

  • Volume: 49, Issue: 3, page 446-464
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Mordukhovich, Boris S., and Outrata, Jiří V.. "Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification." Kybernetika 49.3 (2013): 446-464. <http://eudml.org/doc/260735>.

@article{Mordukhovich2013,
abstract = {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.},
author = {Mordukhovich, Boris S., Outrata, Jiří V.},
journal = {Kybernetika},
keywords = {variational analysis; second-order theory; generalized differentiation; tilt stability; tilt stability; noninear programming; local minimizers; variational analysis; optimality conditions},
language = {eng},
number = {3},
pages = {446-464},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification},
url = {http://eudml.org/doc/260735},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Mordukhovich, Boris S.
AU - Outrata, Jiří V.
TI - Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 3
SP - 446
EP - 464
AB - 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.
LA - eng
KW - variational analysis; second-order theory; generalized differentiation; tilt stability; tilt stability; noninear programming; local minimizers; variational analysis; optimality conditions
UR - http://eudml.org/doc/260735
ER -

References

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