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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 4, Pages 597–615
DOI: https://doi.org/10.31857/S0044466922040135 (Mi zvmmf11384) 		 
Optimal control

Primal–dual Newton method with steepest descent for the linear semidefinite programming problem: iterative process

V. G. Zhadanab

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
DOI: https://doi.org/10.31857/S0044466922040135
Abstract: The primal–dual Newton method for solving the linear semidefinite programming problem is considered. Both primal and weak dual variables may be rank-deficient and belong to the boundaries of feasible sets. Formulas for determining the displacement directions are presented, and properties of these directions are investigated. A technique for selecting the displacement steps that leads to decreasing the rank of the symmetrized product of the primal and weak dual variables is described.
Key words: linear semidefinite programming problem, primal-dual Newton method, iterative process, steepest descent.
Funding agency Grant number
Russian Science Foundation 21-71-30005
This work was supported by the Russian Science Foundation, project no. 21-71-30005.
Received: 02.04.2021
Revised: 02.04.2021
Accepted: 16.12.2021
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 4, Pages 581–598
DOI: https://doi.org/10.1134/S0965542522040133
Bibliographic databases:
Document Type: Article
UDC: 519.658
Language: Russian
Citation: V. G. Zhadan, “Primal–dual Newton method with steepest descent for the linear semidefinite programming problem: iterative process”, Zh. Vychisl. Mat. Mat. Fiz., 62:4 (2022), 597–615; Comput. Math. Math. Phys., 62:4 (2022), 581–598
Citation in format AMSBIB
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\by V.~G.~Zhadan
\paper Primal–dual Newton method with steepest descent for the linear semidefinite programming problem: iterative process
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 4
\pages 597--615
\mathnet{http://mi.mathnet.ru/zvmmf11384}
\crossref{https://doi.org/10.31857/S0044466922040135}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=585285}
\elib{https://elibrary.ru/item.asp?id=48340796}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 4
\pages 581--598
\crossref{https://doi.org/10.1134/S0965542522040133}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85130835134}
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