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A Full-Newton Step Infeasible Interior-Point Algorithm Based on Darvay Directions for Linear Optimization

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Journal of Mathematical Modelling and Algorithms in Operations Research

Abstract

We present a full-Newton step primal-dual infeasible interior-point algorithm based on Darvay’s search directions. These directions are obtained by an equivalent algebraic transformation of the centering equation. The algorithm decreases the duality gap and the feasibility residuals at the same rate. During this algorithm we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Each main iteration of the algorithm consists of a feasibility step and some centering steps. The starting point in the first iteration of the algorithm depends on a positive number ξ and it is strictly feasible for a perturbed pair, and feasibility steps find strictly feasible iterate for the next perturbed pair. By using centering steps for the new perturbed pair, we obtain strictly feasible iterate close to the central path of the new perturbed pair. The algorithm finds an ϵ-optimal solution or detects infeasibility of the given problem. The iteration bound coincides with the best known iteration bound for linear optimization problems.

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Authors and Affiliations

  1. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    K. Ahmadi, F. Hasani & B. Kheirfam

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  1. K. Ahmadi
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  2. F. Hasani
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  3. B. Kheirfam
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Correspondence to B. Kheirfam.

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Ahmadi, K., Hasani, F. & Kheirfam, B. A Full-Newton Step Infeasible Interior-Point Algorithm Based on Darvay Directions for Linear Optimization. J Math Model Algor 13, 191–208 (2014). https://doi.org/10.1007/s10852-013-9227-7

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  • DOI: https://doi.org/10.1007/s10852-013-9227-7

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