Constructive generalization of classical sufficient second-order optimality conditions

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Abstract


In this paper, we consider new sufficient conditions of optimality of the second-order for equality constrained optimization problems, which essentially enhance and complement the classical ones and are constructive. For example, they establish equivalence between sufficient conditions in the equality constrained optimization problems and sufficient conditions for optimality in equality constrained problems by reducing the latter to equalities with the help of introducing slack variables. Previously, when using the classical sufficient optimality conditions, this fact was not considered to be true, that is, the existing classical sufficient conditions were not complete, so the proposed optimality conditions complement the classical ones and close the question of the equivalence of the problems with inequalities and the problems with equalities when reducing the first to the second by introducing slack variables.


About the authors

Yu. G. Evtushenko

Dorodnitsyn Computing Centre, Federal Research Center Computer Science and Control of the Russian Academy of Sciences; Moscow Institute of Physics and Technology; Moscow Aviation Institute (National Research University)

Author for correspondence.
Email: yuri-evtushenko@yandex.ru

Russian Federation, 40, Vavilova street, Moscow, 119333; 9, Institutskij, Dolgoprudny, Moscow region, 141701; 4, Volokolamskoe shosse, Moscow, 125993

Academicaian of the Russian Academy of Sciences

A. A. Tret’yakov

Dorodnitsyn Computing Centre, Federal Research Center Computer Science and Control of the Russian Academy of Sciences; System Research Institute of the Polish Academy of Sciences; Siedlce University

Email: tret@ap.siedlce.pl

Russian Federation, 40, Vavilova street, Moscow, 119333; 6, Newelska str., Warszawa, Poland, 00-001; 2, Konarskiego str., Siedlce, Poland, 08-110

References

  1. Евтушенко Ю. Г. Методы решения экстремальных задач и их применение в системах оптимизации. М.: Наука, 1982. 432 с.
  2. Поляк Б. Т. Введение в оптимизацию. М.: Наука. Гл. ред. физ.-мат. лит., 1983.
  3. Брежнева О. А., Евтушенко Ю. Г., Третьяков А. А. 2-фактор-метод модифицированных функций Лагранжа для решения вырожденных задач условной оптимизации // ДАН. 2006. Т. 408. № 4. С. 439-442.
  4. Bertsekas D. P. Nonlinear Programming. Belmont: Athena Scientific, 1999. P. 191-276.
  5. Brezhneva O. A., Tret’yakov A. A. The p-Factor Lagrange Methods for Degenerate Nonlinear Programming // Numerical Functional Analysis and Optimization. 2007. V. 28. № 9/10. P. 1051-1086.

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