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A Guided Tour in Constraint Qualifications for Nonlinear Programming under Differentiability Assumptions

Author

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  • Giorgio Giorgi

    (Department of Economics and Management, University of Pavia)

Abstract

It is well-known that the celebrated Kuhn-Tucker or Karush-Kuhn-Tucker necessary optimality conditions hold at a local solution point of a nonlinear programming problem if some regularity conditions, usually called "constraint qualifcations", are satisfied. In the present paper we give an up-to-date overview of several constraint quali?cations proposed in the literature for a nonlinear programming problem, under differentiability assumptions. In particular, we point out the various implications existing among the constraint qualifications considered. For the reader's convenience we shall consider separately the case of inequality constraints only and the case of mixed equality and inequality constraints. Some remarks on second-order constraint qualifications are made and some historical notes on this subject are given.

Suggested Citation

  • Giorgio Giorgi, 2018. "A Guided Tour in Constraint Qualifications for Nonlinear Programming under Differentiability Assumptions," DEM Working Papers Series 160, University of Pavia, Department of Economics and Management.
    • Handle: RePEc:pav:demwpp:demwp0160
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    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0160.pdf
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    References listed on IDEAS

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    Cited by:

    1. Giorgio Giorgi, 2019. "Notes on Constraint Qualifications for Second-Order Optimality Conditions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(5), pages 16-32, October.
    2. G. Haeser & A. Ramos, 2020. "New Constraint Qualifications with Second-Order Properties in Nonlinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 494-506, February.

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