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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 2, Pages 232–248
DOI: https://doi.org/10.31857/S0044466922020132 (Mi zvmmf11357) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Optimal control

Primal–dual Newton method with steepest descent for the linear semidefinite programming problem: Newton's system of equations

V. G. Zhadanab

a Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 117333, Moscow, Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
Citations (7)
DOI: https://doi.org/10.31857/S0044466922020132
Abstract: The linear semidefinite programming problem is considered. It is proposed to solve it using a feasible primal–dual method based on solving the system of equations describing the optimality conditions in the problem by Newton’s method. The selection of Newton’s displacement directions in the case when the current points of the iterative process lie on the boundaries of feasible sets is discussed. The partition of the space of symmetric matrices into subspaces is essentially used.
Key words: linear semidefinite programming problem, optimality conditions, primal–dual Newton's method, 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: 12.10.2021
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 2, Pages 232–247
DOI: https://doi.org/10.1134/S0965542522020129
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: Newton's system of equations”, Zh. Vychisl. Mat. Mat. Fiz., 62:2 (2022), 232–248; Comput. Math. Math. Phys., 62:2 (2022), 232–247
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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