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The Homogeneous Self-Dual Method

In: Linear Programming

Author

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  • Robert J. Vanderbei

    (Princeton University)

Abstract

In Chapter 18, we described and analyzed an interior-point method called the path-following algorithm. This algorithm is essentially what one implements in practice but as we saw in the section on convergence analysis, it is not easy (and perhaps not possible) to give a complete proof that the method converges to an optimal solution. If convergence were completely established, the question would still remain as to how fast is the convergence. In this chapter, we shall present a similar algorithm for which a complete convergence analysis can be given.

Suggested Citation

  • Robert J. Vanderbei, 2008. "The Homogeneous Self-Dual Method," International Series in Operations Research & Management Science, in: Linear Programming, edition 3, chapter 0, pages 361-381, Springer.
    • Handle: RePEc:spr:isochp:978-0-387-74388-2_22
    DOI: 10.1007/978-0-387-74388-2_22
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    Cited by:

    1. Rehfeldt, Daniel & Hobbie, Hannes & Schönheit, David & Koch, Thorsten & Möst, Dominik & Gleixner, Ambros, 2022. "A massively parallel interior-point solver for LPs with generalized arrowhead structure, and applications to energy system models," European Journal of Operational Research, Elsevier, vol. 296(1), pages 60-71.

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