Optimization Letters

, Volume 13, Issue 8, pp 1969–1984 | Cite as

Two-phase simplex method for linear semidefinite optimization

  • Vitaly ZhadanEmail author
Original Paper


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.


Linear semidefinite programming Extreme points Primal simplex method Two-phase method Local convergence 



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


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dorodnicyn Computing Centre, FRC “Computer Science and Control”Russian Academy of SciencesMoscowRussia

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