On the norm of a dc function

Authors:
Rafael Blanquero;Emilio Carrizosa
Affiliations:
Facultad de Matemáticas, Universidad de Sevilla, Seville, Spain;Facultad de Matemáticas, Universidad de Sevilla, Seville, Spain
Venue:
Journal of Global Optimization
Year:
2010

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Abstract

It is well known that, if a vector-valued function can be written as difference of componentwise convex functions, the norm of such function inherits this property. In this note we show that, if the norm in use is monotonic in the positive orthant and the functions are non-negative, a sharper decomposition can be obtained.