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Computational complexity of a piecewise linear homotopy algorithm

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Abstract

We give a bound on the number of steps required by the piecewise linear algorithm based on component wise homotopy (proposed by the author for structured problems) when solving a linear problem. When the coefficient matrix is symmetric and positive definite, this bound is polynomial inn and linear in the condition number of the matrix. We also investigate the expected value of the bound for a particular distribution of such matrices.

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Authors and Affiliations

  1. Northwestern University, 60201, Evanston, IL, USA

    R. Saigal

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  1. R. Saigal
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Additional information

This research has been partially supported by the grant MCS 80-05154 from the National Science Foundation.

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Saigal, R. Computational complexity of a piecewise linear homotopy algorithm. Mathematical Programming 28, 164–173 (1984). https://doi.org/10.1007/BF02612356

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  • DOI: https://doi.org/10.1007/BF02612356

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