Abstract
The exact homotopy path when seeking the minimum of a convex function is monotonic in the homotopy parameter. This monotonicity is not inherited by the piecewise linear approximations to such paths produced by fixed-point algorithms.
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References
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This research was partially supported by National Science Foundation Grant ENG76-08749.
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Todd, M.J. Piecewise linear paths to minimize convex functions may not be monotonic. Mathematical Programming 17, 106–108 (1979). https://doi.org/10.1007/BF01588230
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DOI: https://doi.org/10.1007/BF01588230