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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 4, Pages 555–577 (Mi zvmmf297)  

This article is cited in 2 scientific papers (total in 2 papers)

Sensitivity of solutions to systems of optimality conditions under the violation of constraint qualifications

A. F. Izmailov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: A survey is given of old and new results on the sensitivity of solutions to systems of optimality conditions with respect to parametric perturbations. Results of this kind play a key role in subtle convergence analysis of various constrained optimization algorithms. General systems of optimality conditions for problems with abstract constraints, Karush–Kuhn–Tucker systems for mathematical programs, and Lagrange systems for problems with equality constraints are examined. Special attention is given to the cases where the traditional constraint qualifications are violated.

Key words: optimality conditions, Karush–Kuhn–Tucker system, Lagrange system, stability, sensitivity, constraint qualification.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:4, 533–554

Bibliographic databases:

Document Type: Article
UDC: 519.626.2
Received: 25.10.2006

Citation: A. F. Izmailov, “Sensitivity of solutions to systems of optimality conditions under the violation of constraint qualifications”, Zh. Vychisl. Mat. Mat. Fiz., 47:4 (2007), 555–577; Comput. Math. Math. Phys., 47:4 (2007), 533–554

Citation in format AMSBIB
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\pages 555--577
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\transl
\jour Comput. Math. Math. Phys.
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\crossref{https://doi.org/10.1134/S096554250704001X}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Izmailov A.F., “Solution sensitivity for Karush-Kuhn-Tucker systems with non-unique Lagrange multipliers”, Optimization, 59:5 (2010), 747–775  crossref  mathscinet  zmath  isi  elib  scopus
    2. Yang L., Chen Ya., Tong X., “A note on local sensitivity analysis for parametric optimization problem”, Pac. J. Optim., 8:1 (2012), 185–195  mathscinet  zmath  adsnasa  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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