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Two-phase simplex method for linear semidefinite optimization

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Abstract

The linear semidefinite programming problem is considered. To solve it, the variant of the primal simplex method, that generalizes the corresponding method for linear programming problems, is proposed. The passage from one extreme point of the feasible set to another one is described. The main attention is given to pivoting in the case, when the extreme point is irregular, i.e. the “triangular” number of rank of the matrix in the basic point is less than number of equality type constraints in the problem. The approach for finding a starting extreme point is proposed too. The local convergence of the method is proven.

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Acknowledgements

This work was supported by the Russian Foundation for Basic Research (Project No. 17-07-00510).

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  1. Dorodnicyn Computing Centre, FRC “Computer Science and Control”, Russian Academy of Sciences, Vaviliva Str., 40, Moscow, Russia, 119333

    Vitaly Zhadan

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  1. Vitaly Zhadan
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Correspondence to Vitaly Zhadan.

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Zhadan, V. Two-phase simplex method for linear semidefinite optimization. Optim Lett 13, 1969–1984 (2019). https://doi.org/10.1007/s11590-018-1333-z

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  • DOI: https://doi.org/10.1007/s11590-018-1333-z

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