Abstract
We present a new class of primal-dual infeasible-interior-point methods for solving linear programs. Unlike other infeasible-interior-point algorithms, the iterates generated by our methods lie in general position in the positive orthant of ℝ2 and are not restricted to some linear manifold. Our methods comprise the following features: At each step, a projection is used to “recenter” the variables to the domainx i s i ≥μ. The projections are separable into two-dimensional orthogonal projections on a convex set, and thus they are seasy to implement. The use of orthogonal projections allows that a full Newton step can be taken at each iteration, even if the result violates the nonnegativity condition. We prove that a short step version of our method converges in polynomial time.
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Research performed while visiting the Institut für Angewandte Mathematik, University of Würzburg, D-87074 Würzburg, Germany, as a Research Fellow of the Alexander von Humboldt Foundation.
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Mizuno, S., Jarre, F. An infeasible-interior-point algorithm using projections onto a convex set. Ann Oper Res 62, 59–80 (1996). https://doi.org/10.1007/BF02206811
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DOI: https://doi.org/10.1007/BF02206811