ON CONSTRAINT QUALIFICATIONS IN MATHEMATICAL PROGRAMMING

UDC 517.977

  • Sirotko Sergey Ivanovich – PhD (Physics and Mathematics), Associate Professor, Assistant Professor, the Department of Informatics. Belarusian State University of Informatics and Radioelectronics (6, P. Brovki str., 220013, Minsk, Republic of Belarus). E-mail:sergeyis@bsuir.by

  • Pashuk Aleksandr Vladimirovich – Senior Lecturer, the Department of Informatics. Belarusian State University of Informatics and Radioelectronics (6, P. Brovki str., 220013, Minsk, Republic of Belarus). E-mail: pashuk@bsuir.by

DOI: https://doi.org/10.52065/2520-6141-2022-254-1-10-14

Key words: constraint qualifications, optimization, Lagrange multipliers.

For citation: Sirotko S. I., Pashuk A. V. On constraint qualifications in mathematical programming. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2021, no. 1 (254), pp. 10–14 (In Russian). DOI: https://doi.org/10.52065/2520-6141-2022-254-1-10-14.

Abstract

Constraint qualifications play an important role in investigation of mathematical programs since they guarantee the validity of the Karush – Kuhn – Tucker necessary optimality conditions. In spite of effectivity of known constraint qualifications there are vast classes of optimization problems in which these conditions are not fulfilled. On the other hand one can point other weaker constraint qualifications which provide the validity of Karush – Kuhn – Tucker conditions. One of such CQs is the relaxed constant positive linear dependence constraint qualification (RCPLD). In this article we propose a modification of RCPLD which allows to weaken the requirements to constraint in mathematical programs. We also prove sufficient conditions of error bound property.

Download

References

  1. Kuhn H. W., Tucker A. W. Nonlinear Programming. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, University of California Press, 1951, pp. 481–492.
  2. Mangasarian O. L., Fromovitz S. The Fritz-John necessary optimality conditions in presence of equality and inequality constraints. Journal of Mathematical Analysis and Applications, 1967, vol. 7, pp. 37–47.
  3. Andreani R., Haeser G., Schuverdt M.L., Silva P. J. S. A relaxed constant positive linear dependence constraint qualification and applications. Mathematical Programming, 2012, vol. 135, pp. 255–273.
  4. Pang J. Error bounds in mathematical programming. Mathematical Programming, 1997, vol. 79, pp. 299–332.
  5. Luderer B., Minchenko L, Satsura T. Multivalued analysis and nonlinear programming problems with perturbations. Dordrecht, Kluwer Academic Publisher, 2002. 220 p.
  6. Kruger A. Y. Error Bounds and Metric Subregularity. Optimization, 2015, vol. 64, no. 1, pp. 49–79.
  7. Fabian M. J., Henrion R., Kruger A. Y., Outrata J. V. Error bounds: necessary and sufficient conditions. Set-Valued and Variational Analysis, 2010, vol. 18, no. 2, pp. 121–149.
  8. Kruger A. Y., Minchenko L. I., Outrata J. V. On relaxing the Mangasarian-Fromovitz constraint qualification. Positivity, 2014, vol. 18, pp. 171–189.
  9. Minchenko L. I. Note on MFCQ-like constraint qualifications. Journal of Optimization Theory and Applications, 2019, vol. 182, no. 3, pp. 1199–1204.
  10. Bednarchuk E. M., Minchenko L. I., Rutkowski K. E. On Lipschitz-like continuity of a class of setvalued mappings. Optimization, 2020, vol. 69, no. 12, pp. 2535–2549.
  11. Minchenko L., Stakhovski S. Parametric nonlinear programming problems under relaxed constant rank regularity condition. SIAM Journal on Optimization, 2011, vol. 21, no. 1, pp. 314–332.
04.01.2022