Enlarging neighborhoods of interior-point algorithms for linear programming via least values of proximity measure functions

Authors:
Y. B. Zhao
Affiliations:
Institute of Applied Mathematics, AMSS, Chinese Academy of Science, Beijing 100080, China
Venue:
Applied Numerical Mathematics
Year:
2007

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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.