A new polynomial-time algorithm for linear programming
Combinatorica
Convergence behavior of interior-point algorithms
Mathematical Programming: Series A and B
A primal-dual infeasible-interior-point algorithm for linear programming
Mathematical Programming: Series A and B
On polynomiality of the Mehrotra-type predictor-corrector interior-point algorithms
Mathematical Programming: Series A and B
Primal-dual interior-point methods
Primal-dual interior-point methods
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
On Mehrotra-Type Predictor-Corrector Algorithms
SIAM Journal on Optimization
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Based on the good computational results of the feasible version of the Mehrotra's predictor-corrector variant algorithm presented by Bastos and Paixão, in this paper we discuss its complexity. We prove the efficiency of this algorithm by showing its polynomial complexity and, consequently, its Q-linearly convergence. We start by proving some technical results which are used to discuss the step size estimate of the algorithm. It is shown that, at each iteration, the step size computed by this Mehrotra's predictor-corrector variant algorithm is bounded below, for n≥2, by $\frac{1}{200 n^4};$ consequently proving that the algorithm has O(n4 |log(ε)|) iteration complexity.