Abstract
It is well known that a wide-neighborhood interior-point algorithm for linear programming performs much better in implementation than its small-neighborhood counterparts. In this paper, we provide a unified way to enlarge the neighborhoods of predictor–corrector interior-point algorithms for linear programming. We prove that our methods not only enlarge the neighborhoods but also retain the so-far best known iteration complexity and superlinear (or quadratic) convergence of the original interior-point algorithms. The idea of our methods is to use the global minimizers of proximity measure functions.
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