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Note on Mangasarian–Fromovitz-Like Constraint Qualifications

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Abstract

We consider constraint qualifications in nonlinear programming which can be reduced to the classical Mangasarian–Fromovitz condition with the help of a new parametrization of the set of feasible points.

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References

  1. Kuhn, H.W., Tucker, A.W.: Nonlinear programming. In: Neyman, J. (ed.) Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481–492. University of California Press, Berkeley (1951)

    Google Scholar 

  2. Mangasarian, O.L., Fromovitz, S.: The Fritz-John necessary optimality conditions in presence of equality and inequality constraints. J. Math. Anal. Appl. 7, 37–47 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  3. Janin, R.: Directional derivative of the marginal function in nonlinear programming. Math. Program. Study 21, 110–126 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  4. Minchenko, L.I., Stakhovski, S.M.: On relaxed constant rank regularity condition in mathematical programming. Optimization 60, 429–440 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Minchenko, L., Stakhovski, S.: About generalizing the Mangasarian–Fromovitz regularity condition. Dokl. BGUIR 8, 104–109 (2010). (in Russian)

    Google Scholar 

  6. Kruger, A.Y., Minchenko, L.I., Outrata, J.V.: On relaxing the Mangasarian–Fromovitz constraint qualification. Positivity 18, 171–189 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. Andreani, R., Haeser, G., Schuverdt, M.L., Silva, P.J.S.: Two new weak constraint qualifications and applications. SIAM J. Optim. 22, 1109–1125 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Andreani, R., Martinez, J.M., Schuverdt, M.L.: On the relations between constant positive linear dependence condition and quasinormality constraint qualification. J. Optim. Theory Appl. 125, 473–485 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Andreani, R., Haeser, G., Schuverdt, M.L., Silva, P.J.S.: A relaxed constant positive linear dependence constraint qualification and applications. Math. Program. 135, 255–273 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Giannessi, F.: Constrained Optimization and Image Space Analysis, Separation of Sets and Optimality Conditions, vol. 1. Springer, New York (2005)

    MATH  Google Scholar 

  11. Moldovan, A., Pellegrini, L.: On regularity for constrained extremum problems. Part 2: necessary optimality conditions. J. Optim. Theory Appl. 142, 165–183 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Guo, L., Zhang, J., Lin, G.-H.: New results on constraint qualifications for nonlinear extremum problems and extensions. J. Optim. Theory Appl. 163, 737–754 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lu, S.: Implications of the constant rank constraint qualification. Math. Program. 126, 365–392 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lu, S.: Relation between the constant rank and the relaxed constant rank constraint qualifications. Optimization 61, 555–566 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Gorokhovik, V.V.: Finite-Dimensional Optimization Problems. BSU Publishing, Minsk (2007)

    MATH  Google Scholar 

  16. Zorich, V.A.: Mathematical Analysis, P. 1. Springer, Berlin (2004)

    Google Scholar 

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Acknowledgements

This research was supported by Belarussian State Program for Fundamental Research “Mathematical Simulation Methods to Complicated Systems”

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Correspondence to Leonid Minchenko.

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Minchenko, L. Note on Mangasarian–Fromovitz-Like Constraint Qualifications. J Optim Theory Appl 182, 1199–1204 (2019). https://doi.org/10.1007/s10957-019-01519-6

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  • DOI: https://doi.org/10.1007/s10957-019-01519-6

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