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m v2.05b - Bot T20 CW#61 - Fix errors for CW project (Reference before punctuation - Heading start with three "=" and later with level two) |
Citation bot (talk | contribs) Altered title. Add: chapter-url, chapter. Removed or converted URL. | Use this bot. Report bugs. | Suggested by Abductive | Category:Optimization of ordered sets | #UCB_Category 3/3 |
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=== Definition ===
Let <math>S</math> be a finite set. A set function <math>f: 2^S \to \mathbb{R}</math> is '''supermodular''' if it satifies the following (equivalent) conditions:<ref>{{Citation |last=McCormick |first=S. Thomas |title=Discrete Optimization |chapter=Submodular Function Minimization |date=2005 |series=Handbooks in Operations Research and Management Science |volume=12 |pages=321–391 |chapter-url=https://linkinghub.elsevier.com/retrieve/pii/S0927050705120076 |access-date=2024-12-12 |publisher=Elsevier |language=en |doi=10.1016/s0927-0507(05)12007-6 |isbn=978-0-444-51507-0}}</ref>
# <math> f(A)+f(B) \leq f(A \cap B) + f(A \cup B) </math> for all <math> A, B \subseteq S </math>.
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