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Definition 24

[17Y]Let \(CβŠ‚ ℝ^ n\) be a convex set, and \(f:C→ℝ\) a function. \(f\) is convex if

\[ βˆ€ t∈[0,1],~ ~ βˆ€ x,y∈ C, ~ ~ f\big(tx+(1-t)y\big)≀ tf(x)+(1-t)f(y)~ ~ . \]

\(f\) is strictly convex if also

\[ βˆ€ t∈(0,1),~ ~ βˆ€ x,y∈ C, xβ‰  y, ~ ~ f\big(tx+(1-t)y\big){\lt} tf(x)+(1-t)f(y)~ ~ . \]

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Authors: "Mennucci , Andrea C. G." .
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  • convex function
  • convex function
  • strictly convex function
  • function, convex , see convex function
  • function, strictly convex , see strictly convex function
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