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23-1523.pdf

en

Definition 1 Ā· DR-submodular function

2.1 Notations and Definitions

Given a convex set š’Ÿ āŠ† ā„įµˆ, a continuous function f : ā„įµˆ → ā„ is said to be DR-submodular over š’Ÿ, if for any x ≤ y ∈ š’Ÿ and a ∈ ā„ā‚Š …

f(x + aeįµ¢) āˆ’ f(x) ≄ f(y + aeįµ¢) āˆ’ f(y)

and x ≤ y means xįµ¢ ≤ yįµ¢, āˆ€i ∈ [d].

Reading version

2.1 Ā· Notations and definitions

2.1 Notations and Definitions

Given a convex set š’Ÿ āŠ† ā„įµˆ, a continuous function f : ā„įµˆ → ā„ is said to be DR-submodular over š’Ÿ, if for any x ≤ y ∈ š’Ÿ and a ∈ ā„ā‚Š …

f(x + aeįµ¢) āˆ’ f(x) ≄ f(y + aeįµ¢) āˆ’ f(y)

and x ≤ y means xįµ¢ ≤ yįµ¢, āˆ€i ∈ [d].

Paper excerpt and explanatory demonstration adapted from DR-submodularity Ā· Lian et al., JMLR 2024 Ā· CC BY 4.0

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