Primal-Dual Newton’s Method with Steepest Descent for Linear Programming

  • Vitaly ZhadanEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)


The primal-dual method for solving linear programming problems is considered. In order to determine the search directions the non-perturbed system of optimality conditions is solved by Newton’s method. If this system is degenerate, then an auxiliary linear complementarity problem is solved for obtained unique directions. Starting points and all consequent points are feasible. The step-lengths are chosen from the steepest descent approach based on minimization of the dual gap. The safety factor is not introduced, and trajectories are allowed to move along the boundaries of the feasible sets. The convergence of the method at a finite number of iterations is proved.


Linear programming Primal-dual method Newton’s method Steepest descent Finite convergence 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dorodnicyn Computing Centre, FRC “Computer Science and Control” of RASMoscowRussia

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