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Primal–Dual Newton Method with Steepest Descent for the Linear Semidefinite Programming Problem: Newton’s System of Equations

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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.

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Funding

This work was supported by the Russian Science Foundation (project no. 21-71-30005).

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Authors and Affiliations

  1. Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, 117333, Moscow, Russia

    V. G. Zhadan

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  1. V. G. Zhadan
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Correspondence to V. G. Zhadan.

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The author declares that he has no conflicts of interest.

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Translated by A. Klimontovich

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Zhadan, V.G. Primal–Dual Newton Method with Steepest Descent for the Linear Semidefinite Programming Problem: Newton’s System of Equations. Comput. Math. and Math. Phys. 62, 232–247 (2022). https://doi.org/10.1134/S0965542522020129

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  • DOI: https://doi.org/10.1134/S0965542522020129

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