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On Error Bounds for Quasinormal Programs

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Abstract

The Mangasarian-Fromovitz constraint qualification is a central concept within the theory of constraint qualifications in nonlinear optimization. Nevertheless there are problems where this condition does not hold though other constraint qualifications can be fulfilled. One of such constraint qualifications is the so-called quasinormality by Hestenes. The well known error bound property (R-regularity) can also play the role of a general constraint qualification providing the existence of Lagrange multipliers. In this note we investigate the relation between some constraint qualifications and prove that quasinormality implies the error bound property, while the reciprocal is not true.

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Authors and Affiliations

  1. Department of Informatics, Belorussian State University of Informatics and Radioelectronics, Minsk, Belarus

    L. Minchenko & A. Tarakanov

Authors
  1. L. Minchenko
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  2. A. Tarakanov
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Correspondence to L. Minchenko.

Additional information

Communicated by F. Giannessi.

This research was supported by Belorussian Republican Foundation for Fundamental Research and State Programs for Fundamental Research “Mathematical Models” and “Mathematical Methods”.

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Minchenko, L., Tarakanov, A. On Error Bounds for Quasinormal Programs. J Optim Theory Appl 148, 571–579 (2011). https://doi.org/10.1007/s10957-010-9768-0

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