Constructive generalization of classical sufficient second-order optimality conditions
- Authors: Evtushenko Y.G.1,2,3, Tret’yakov A.A.1,4,5
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Affiliations:
- 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)
- System Research Institute of the Polish Academy of Sciences
- Siedlce University
- Issue: Vol 487, No 5 (2019)
- Pages: 493-495
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/15886
- DOI: https://doi.org/10.31857/S0869-56524875493-495
- ID: 15886
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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
Academicaian of the Russian Academy of Sciences
Russian Federation, 40, Vavilova street, Moscow, 119333; 9, Institutskij, Dolgoprudny, Moscow region, 141701; 4, Volokolamskoe shosse, Moscow, 125993A. 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
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