Abstract
A specific property of convex functions, which is called the diff-max property, plays an important role in some aspects of optimization. This paper shows that in a finite dimensional space a closed proper convex function has this property if and only if it is locally polyhedral. A preliminary study of closed locally polyhedral convex sets is provided and a survey of some applications of the diff-max property in optimization is given.
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© 1988 Birkhäuser Verlag Basel
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Durier, R. (1988). On Locally Polyhedral Convex Functions. In: Hoffmann, KH., Zowe, J., Hiriart-Urruty, JB., Lemarechal, C. (eds) Trends in Mathematical Optimization. International Series of Numerical Mathematics/Internationale Schriftenreihe zur Numerischen Mathematik/Série internationale d’Analyse numérique, vol 84. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9297-1_4
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DOI: https://doi.org/10.1007/978-3-0348-9297-1_4
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9984-0
Online ISBN: 978-3-0348-9297-1
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