A short proof for stronger version of DS decomposition in set function optimization

Xiang Li () and H. George Du ()
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Xiang Li: Santa CLara University
H. George Du: University of Texas at Austin

Journal of Combinatorial Optimization, 2020, vol. 40, issue 4, No 4, 906 pages

Abstract: Abstract Using a short proof, we show that every set function f can be decomposed into the difference of two monotone increasing and strictly submodular functions g and h, i.e., $$f=g-h$$ f = g - h , and every set function f can also be decomposed into the difference of two monotone increasing and strictly supermodular functions g and h, i.e., $$f=g-h$$ f = g - h .

Keywords: Set function; DS decomposition; Monotone nondecreasing; Submodular; Supermodular (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10878-020-00639-4

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