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The p-th Order Necessary Optimality Conditions for Inequality—Constrained Optimization Problems

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Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2667))

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Abstract

In this paper, we consider a nonlinear optimization problem with inequality constraints. The paper addresses the degenerate case when the active constraint gradients are linearly dependent at the solution, and the Mangasarian-Fromovitz constraint qualification fails to hold. For this case, we present new generalized p-order necessary optimality conditions. The conditions subsume the classical conditions and give new and nontrivial conditions for the degenerate case. The presented results can be considered as a part of the p-regularity theory.

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References

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Author information

Authors and Affiliations

  1. Institute for Mathematics and its Applications, University of Minnesota, 400 Lind Hall, 207 Church St. SE, Minneapolis, MN, 55455

    Olga Brezhneva

  2. Computing Center of the Russian Academy of Sciences, Vavilova 40, Moscow, GSP-1, Russia

    Alexey Tret’yakov

  3. University of Podlasie in Siedlce, 3 Maja, Siedlce, Poland

    Alexey Tret’yakov

Authors
  1. Olga Brezhneva
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  2. Alexey Tret’yakov
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA

    Vipin Kumar

  2. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  3. Heuchera Technologies Inc., 122 9251-8 Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  4. Département d’informatique et de recherche opérationelle, Université de Montréal, Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

  5. Department of Computer Science and Engineering, University of Minessota, MN, 55455, USA

    Vipin Kumar

  6. The Queen’s University of Belfast, School of Computer Science, Belfast BT7 1NN, Northern Ireland, UK

    Chih Jeng Kenneth Tan

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© 2003 Springer-Verlag Berlin Heidelberg

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Brezhneva, O., Tret’yakov, A. (2003). The p-th Order Necessary Optimality Conditions for Inequality—Constrained Optimization Problems. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44839-X_95

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  • DOI: https://doi.org/10.1007/3-540-44839-X_95

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40155-1

  • Online ISBN: 978-3-540-44839-6

  • eBook Packages: Springer Book Archive

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