Simplified O(nL) infeasible interior-point algorithm for linear optimization using full-Newton steps

Authors:
H. Mansouri;C. Roos
Affiliations:
Department of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, GA, The Netherlands;Department of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, GA, The Netherlands
Venue:
Optimization Methods & Software
Year:
2007

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Abstract

In Roos [Roos, C., 2006, A full-Newton step O(n) infeasible interior-point algorithm for linear optimization. SIAM Journal on Optimization, 16(4), 1110-1136.] presented a new primal-dual infeasible interior-point algorithm that uses full-Newton steps and whose iteration bound coincides with the best-known bound for infeasible interior-point algorithms. Each iteration consists of a step that restores the feasibility for an intermediate problem (the so-called feasibility step) and a few (usual) centering steps. No more than O(nlog(n/ε)) iterations are required for getting an ε-solution of the problem at hand, which coincides with the best-known bound for infeasible interior-point algorithms. In this article, we introduce a different feasibility step and show that the same complexity result can be obtained with a relatively simpler analysis.