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“Cone-free” primal-dual path-following and potential-reduction polynomial time interior-point methods

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Abstract.

We present a framework for designing and analyzing primal-dual interior-point methods for convex optimization. We assume that a self-concordant barrier for the convex domain of interest and the Legendre transformation of the barrier are both available to us. We directly apply the theory and techniques of interior-point methods to the given good formulation of the problem (as is, without a conic reformulation) using the very usual primal central path concept and a less usual version of a dual path concept. We show that many of the advantages of the primal-dual interior-point techniques are available to us in this framework and therefore, they are not intrinsically tied to the conic reformulation and the logarithmic homogeneity of the underlying barrier function.

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Authors and Affiliations

  1. Faculty of IE&M, Technion, Haifa, Israel

    Arkadi Nemirovski

  2. Dept. of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Canada

    Levent Tunçel

Authors
  1. Arkadi Nemirovski
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  2. Levent Tunçel
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Correspondence to Levent Tunçel.

Additional information

Part of the research was done while the author was a Visiting Professor at the University of Waterloo.

Research of this author is supported in part by a PREA from Ontario and by a NSERC Discovery Grant. Tel: (519) 888-4567 ext.5598, Fax: (519) 725-5441

Mathematics Subject Classification (2000): 90C51, 90C25, 65Y20,90C28, 49D49

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Nemirovski, A., Tunçel, L. “Cone-free” primal-dual path-following and potential-reduction polynomial time interior-point methods. Math. Program. 102, 261–294 (2005). https://doi.org/10.1007/s10107-004-0545-4

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  • DOI: https://doi.org/10.1007/s10107-004-0545-4

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