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

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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.

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Authors and Affiliations

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

    A. F. Izmailov

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  1. A. F. Izmailov
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Original Russian Text © A.F. Izmailov, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 4, pp. 555–577.

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Izmailov, A.F. Sensitivity of solutions to systems of optimality conditions under the violation of constraint qualifications. Comput. Math. and Math. Phys. 47, 533–554 (2007). https://doi.org/10.1134/S096554250704001X

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  • DOI: https://doi.org/10.1134/S096554250704001X

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