Abstract
In this paper we propose a long-step target-following methodology for linear programming. This is a general framework, that enables us to analyze various long-step primal-dual algorithms in the literature in a short and uniform way. Among these are long-step central and weighted path-following methods and algorithms to compute a central point or a weighted center. Moreover, we use it to analyze a method with the property that starting from an initial noncentral point, generates iterates that simultaneously get closer to optimality and closer to centrality.
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This work is completed with the support of a research grant from SHELL.
The first author is supported by the Dutch Organization for Scientific Research (NWO), grant 611-304-028.
The fourth author is supported by the Swiss National Foundation for Scientific Research, grant 12-34002.92.
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Jansen, B., Roos, C., Terlaky, T. et al. Long-step primal-dual target-following algorithms for linear programming. Mathematical Methods of Operations Research 44, 11–30 (1996). https://doi.org/10.1007/BF01246327
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DOI: https://doi.org/10.1007/BF01246327