# Quick TutorialΒΆ

Consider a constrained least squares problem

\[\begin{split}\begin{array}{ll}
\mbox{minimize} & \|Ax - b\|_2^2 \\
\mbox{subject to} & x \geq 0
\end{array}\end{split}\]

with variable \(x\in \mathbf{R}^{n}\), and problem data \(A \in \mathbf{R}^{m \times n}\), \(b \in \mathbf{R}^{m}\).

This problem can be solved in Convex.jl as follows:

```
# Make the Convex.jl module available
using Convex
# Generate random problem data
m = 4; n = 5
A = randn(m, n); b = randn(m, 1)
# Create a (column vector) variable of size n x 1.
x = Variable(n)
# The problem is to minimize ||Ax - b||^2 subject to x >= 0
# This can be done by: minimize(objective, constraints)
problem = minimize(sum_squares(A * x - b), [x >= 0])
# Solve the problem by calling solve!
solve!(problem)
# Check the status of the problem
problem.status # :Optimal, :Infeasible, :Unbounded etc.
# Get the optimum value
problem.optval
```