Convex Function

Last updated Nov 1, 2022

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 $x,y \in S$ $$f(\lambda x + (1-\lambda) y) \leq \lambda f(x) + (1- \lambda) f(y)$$

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

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