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Error bounds for the aggregated convex programming problem

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Abstract

Applied mathematical programming problems are often approximations of larger, more detailed problems. One criterion to evaluate an approximating program is the magnitude of the difference between the optimal objective values of the original and the approximating program. The approximation we consider is variable aggregation in a convex program. Bounds are derived on the difference between the two optimal objective values. Previous results of Geoffrion and Zipkin are obtained by specializing our results to linear programming. Also, we apply our bounds to a convex transportation problem.

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Authors and Affiliations

  1. Graduate School of Business, University of Chicago, Chicago, IL, USA

    Gur Huberman

Authors
  1. Gur Huberman
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Additional information

Thanks are due to Ron Dembo, Paul Zipkin and the referees for valuable comments. This research was supported by NSF Grant ENG-76-15599.

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Huberman, G. Error bounds for the aggregated convex programming problem. Mathematical Programming 26, 100–108 (1983). https://doi.org/10.1007/BF02591896

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  • DOI: https://doi.org/10.1007/BF02591896

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