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An alternating linearization bundle method for convex optimization and nonlinear multicommodity flow problems

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Abstract

We give a bundle method for minimizing the sum of two convex functions, one of them being known only via an oracle of arbitrary accuracy. Each iteration involves solving two subproblems in which the functions are alternately represented by their linearizations. Our approach is motivated by applications to nonlinear multicommodity flow problems. Encouraging numerical experience on large scale problems is reported.

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Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    K. C. Kiwiel

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  1. K. C. Kiwiel
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Correspondence to K. C. Kiwiel.

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Research supported by the Polish Ministry of Science and Higher Education Grant No. N N514 408736.

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Kiwiel, K.C. An alternating linearization bundle method for convex optimization and nonlinear multicommodity flow problems. Math. Program. 130, 59–84 (2011). https://doi.org/10.1007/s10107-009-0327-0

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  • DOI: https://doi.org/10.1007/s10107-009-0327-0

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