Abstract
A finite descent algorithm is derived based on an explicit parametrization of the subdifferential of the polyhedral convex function by using continuation applied to its proximal transform. A method for resolving degeneracy is sketched as are certain points relating to implementation. Applications have been made to linear programming, both directly and by the use of penalty methods, to ℓ1 and ℓ∞ fitting problems, and to the interesting and challenging rank regression problem.
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© 1983 Springer-Verlag Berlin Heidelberg
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Osborne, M.R. (1983). An Algorithm for Minimizing Polyhedral Convex Functions. In: Fiacco, A.V., Kortanek, K.O. (eds) Semi-Infinite Programming and Applications. Lecture Notes in Economics and Mathematical Systems, vol 215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46477-5_12
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DOI: https://doi.org/10.1007/978-3-642-46477-5_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12304-0
Online ISBN: 978-3-642-46477-5
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