2010/11/30 by Carola Schrage · 1 citation
Mathematics · #math.OC #msc:49N15 #msc:54C60 #msc:90C46
paper · pdf · doi:10.1080/02331934.2012.741126
arXiv admin note: substantial text overlap with arXiv:1012.4357
arxiv created 2012/06/20 · arxiv updated 2014/05/29
To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. Using this conjugate, weak and strong duality results are proven.