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Concise representation of generalised gradients

Published online by Cambridge University Press:  17 February 2009

M. R. Osborne ,
S. A. Pruess  and
R. S. Womersley
M. R. Osborne
Affiliation:
Department of Statistics, IAS, Australian National University, Canberra 2601
S. A. Pruess
Affiliation:
Department of Mathematics and Statistics, University of New Maxico
R. S. Womersley
Affiliation:
School of Mathematics, Univ. of New South Wales, Kennington 2033
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Computing the generalised gradient directly using its standard definition can involve forming the convex hull of a very large number of vectors. Here an alternative concise parametrization is developed for the generalised gradient of the signed rank regression family of objective functions, a class of piecewise linear functions which includes both convex and nonconvex members. The approach uses the geometry of the epigraph explicitly and this suggests extensions to more general functions. A nondegeneracy condition is assumed which is natural in optimization problems.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 1 , July 1986 , pp. 57 - 74
Copyright
Copyright © Australian Mathematical Society 1986

References

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