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A general parametric analysis approach and its implication to sensitivity analysis in interior point methods

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Abstract

Adler and Monteiro (1992) developed a parametric analysis approach that is naturally related to the geometry of the linear program. This approach is based on the availability of primal and dual optimal solutions satisfying strong complementarity. In this paper, we develop an alternative geometric approach for parametric analysis which does not require the strong complementarity condition. This parametric analysis approach is used to develop range and marginal analysis techniques which are suitable for interior point methods. Two approaches are developed, namely the LU factorization approach and the affine scaling approach.

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, 30332-0205, Atlanta, GA, USA

    Renato D. C. Monteiro

  2. Department of IE/MS, Northwestern University, 60208, Evanston, IL, USA

    Sanjay Mehrotra

Authors
  1. Renato D. C. Monteiro
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  2. Sanjay Mehrotra
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Additional information

Supported by the National Science Foundation (NSF) under Grant No. DDM-9109404 and Grant No. DMI-9496178. This work was done while the author was a faculty member of the Systems and Industrial Engineering Department at The University of Arizona.

Supported in part by the GTE Laboratories and the National Science Foundation (NSF) under Grant No. CCR-9019469.

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Monteiro, R.D.C., Mehrotra, S. A general parametric analysis approach and its implication to sensitivity analysis in interior point methods. Mathematical Programming 72, 65–82 (1996). https://doi.org/10.1007/BF02592332

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  • DOI: https://doi.org/10.1007/BF02592332

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