# Regularized least-squares

Here we solve some constrained least-squares problems with 1-norm regularization, and plot how the solution changes with increasing regularization.

```
using Random
Random.seed!(1)
m = 25;
n = 10;
A = randn(m, n);
b = randn(m, 1);
```

```
using Convex, SCS, LinearAlgebra
gammas = exp10.(range(-4, stop = 2, length = 100));
x_values = zeros(n, length(gammas));
x = Variable(n);
for i in 1:length(gammas)
cost = sumsquares(A * x - b) + gammas[i] * norm(x, 1)
problem = minimize(cost, [norm(x, Inf) <= 1])
solve!(problem, SCS.Optimizer; silent = true)
x_values[:, i] = evaluate(x)
end
```

Plot the regularization path.

```
using Plots
plot(
title = "Entries of x vs lambda",
xaxis = :log,
xlabel = "lambda",
ylabel = "x",
)
for i in 1:n
plot!(gammas, x_values[i, :], label = "x$i")
end
plot!()
```

*This page was generated using Literate.jl.*