Abstract
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.
This work was supported by the Russian Foundation for Basic Research (project no. 17-07-00510).
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Zhadan, V. (2019). Primal-Dual Newton’s Method with Steepest Descent for Linear Programming. In: Evtushenko, Y., Jaćimović, M., Khachay, M., Kochetov, Y., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2018. Communications in Computer and Information Science, vol 974. Springer, Cham. https://doi.org/10.1007/978-3-030-10934-9_6
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