---
tag: 07GR3TNW4H
kind: concept
name: Convex function on R^n
aliases: [convex-function-several-variables]
msc: [26B25]
uses: [0JPCHTXWG0]
sources:
  - url: https://en.wikipedia.org/wiki/Convex_function
    locator: Definition
---

## Summary

Take a real-valued [[function of several real variables|0JPCHTXWG0]] on a convex set. The function is convex when its graph lies on or below each chord between two points of the graph.
Convex functions are important in optimisation because each local minimum of a convex function is a global minimum.