# Convex Optimization

Discover the power of convex optimization, including its standard form, important properties, and code examples.

## What is convex optimization?

Convex optimization is a mathematical optimization technique that optimizes problems with convex objective functions and constraints.

### Standard form

The standard form of a convex optimization problem is as follows:

$\begin{aligned} \min_{\bold x} \quad & f_0(\bold x)\\ \textrm{s.t.} \quad & f_i(\bold x)\le0 \quad & i=1,2,\dots,m\\ \quad & g_j(\bold x)=0 \quad & j=1,2,\dots,k \\ \end{aligned}$

Here, the objective function $f_0$ and the inequality constraints $f_i$ are all convex, and the equality constraints $g_j$ are linear.

## What is a convex function?

A convex function is a real-valued function

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