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What does SUPERMODULAR FUNCTION stand for?
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What does SUPERMODULAR FUNCTION mean?
- Supermodular function
- In mathematics, a function f : R k → R {\displaystyle f\colon \mathbb {R} ^{k}\to \mathbb {R} } is supermodular if f ( x ↑ y ) + f ( x ↓ y ) ≥ f ( x ) + f ( y ) {\displaystyle f(x\uparrow y)+f(x\downarrow y)\geq f(x)+f(y)} for all x {\displaystyle x} , y ∈ R k {\displaystyle y\in \mathbb {R} ^{k}} , where x ↑ y {\displaystyle x\uparrow y} denotes the componentwise maximum and x ↓ y {\displaystyle x\downarrow y} the componentwise minimum of x {\displaystyle x} and y {\displaystyle y} . If −f is supermodular then f is called submodular, and if the inequality is changed to an equality the function is modular. If f is twice continuously differentiable, then supermodularity is equivalent to the condition ∂ 2 f ∂ z i ∂ z j ≥ 0 for all i ≠ j . {\displaystyle {\frac {\partial ^{2}f}{\partial z_{i}\,\partial z_{j}}}\geq 0{\mbox{ for all }}i\neq j.}
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"SUPERMODULAR FUNCTION." Abbreviations.com. STANDS4 LLC, 2024. Web. 21 Sep. 2024. <https://www.abbreviations.com/SUPERMODULAR%20FUNCTION>.
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