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Convex Function

Last updated Nov 1, 2022

# Definition

Let $V$ be a Vector Space

over

\mathbb{R}

, let

S \subset V

be a Convex Set, and suppose

f: S \to \mathbb{R}

. Then

f

is a Strictly Convex Function if for all

\lambda \in [0, 1]

and all

x,y \in S

f(\lambda x + (1-\lambda) y) \leq \lambda f(x) + (1- \lambda) f(y)

# Remarks

This means that the value of $f$ is below any line segment connecting wrapping points.

# Other Outlinks

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Backlinks

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