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In [1]:



    


srand(1)
m = 25;
n = 10;
A = randn(m, n);
b = randn(m, 1);



    











In [2]:



    


using Convex, SCS
set_default_solver(SCSSolver(verbose=0));
gammas = logspace(-4, 2, 100);
x_values = zeros(n, length(gammas));
x = Variable(n);
for i=1:length(gammas)
    cost = sum_squares(A*x - b) + gammas[i]*norm(x,1);
    problem = minimize(cost, [norm(x, Inf) <= 1]);
    solve!(problem);
    x_values[:,i] = evaluate(x);
end



    











In [3]:



    


# Plot the regularization path.
using Gadfly, DataFrames
df = DataFrame(λ=gammas, x=vec(x_values[1,:]), label="x1")
for i=2:n
    df = vcat(df, DataFrame(λ=gammas, x=vec(x_values[i,:]), label=string("x", i)));
end
plot(df, x="λ", y="x", color="label", Geom.line, Scale.x_log10, Guide.title("Entries of x vs λ"))



    


















    
Out[3]:









  
    λ
  
  
    10-11
    10-10
    10-9
    10-8
    10-7
    10-6
    10-5
    10-4
    10-3
    10-2
    10-1
    100
    101
    102
    103
    104
    105
    106
    107
    108
    109
    10-10.0
    10-9.8
    10-9.6
    10-9.4
    10-9.2
    10-9.0
    10-8.8
    10-8.6
    10-8.4
    10-8.2
    10-8.0
    10-7.8
    10-7.6
    10-7.4
    10-7.2
    10-7.0
    10-6.8
    10-6.6
    10-6.4
    10-6.2
    10-6.0
    10-5.8
    10-5.6
    10-5.4
    10-5.2
    10-5.0
    10-4.8
    10-4.6
    10-4.4
    10-4.2
    10-4.0
    10-3.8
    10-3.6
    10-3.4
    10-3.2
    10-3.0
    10-2.8
    10-2.6
    10-2.4
    10-2.2
    10-2.0
    10-1.8
    10-1.6
    10-1.4
    10-1.2
    10-1.0
    10-0.8
    10-0.6
    10-0.4
    10-0.2
    100.0
    100.2
    100.4
    100.6
    100.8
    101.0
    101.2
    101.4
    101.6
    101.8
    102.0
    102.2
    102.4
    102.6
    102.8
    103.0
    103.2
    103.4
    103.6
    103.8
    104.0
    104.2
    104.4
    104.6
    104.8
    105.0
    105.2
    105.4
    105.6
    105.8
    106.0
    106.2
    106.4
    106.6
    106.8
    107.0
    107.2
    107.4
    107.6
    107.8
    108.0
    10-10
    10-5
    100
    105
    1010
    10-10.0
    10-9.5
    10-9.0
    10-8.5
    10-8.0
    10-7.5
    10-7.0
    10-6.5
    10-6.0
    10-5.5
    10-5.0
    10-4.5
    10-4.0
    10-3.5
    10-3.0
    10-2.5
    10-2.0
    10-1.5
    10-1.0
    10-0.5
    100.0
    100.5
    101.0
    101.5
    102.0
    102.5
    103.0
    103.5
    104.0
    104.5
    105.0
    105.5
    106.0
    106.5
    107.0
    107.5
    108.0
  
  
    
      x1
      x2
      x3
      x4
      x5
      x6
      x7
      x8
      x9
      x10
    
    
      
      
      
      
      
      
      
      
      
      
    
    
      label
    
  
  
    
      
    
    
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
    
    
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
    
    
      
        
        
        
        
        
        
        
        
        
        
      
    
    
      
        
        
      
      
        
      
      
        
      
      
        
        
      
    
  
  
    -3.0
    -2.5
    -2.0
    -1.5
    -1.0
    -0.5
    0.0
    0.5
    1.0
    1.5
    2.0
    2.5
    -2.50
    -2.45
    -2.40
    -2.35
    -2.30
    -2.25
    -2.20
    -2.15
    -2.10
    -2.05
    -2.00
    -1.95
    -1.90
    -1.85
    -1.80
    -1.75
    -1.70
    -1.65
    -1.60
    -1.55
    -1.50
    -1.45
    -1.40
    -1.35
    -1.30
    -1.25
    -1.20
    -1.15
    -1.10
    -1.05
    -1.00
    -0.95
    -0.90
    -0.85
    -0.80
    -0.75
    -0.70
    -0.65
    -0.60
    -0.55
    -0.50
    -0.45
    -0.40
    -0.35
    -0.30
    -0.25
    -0.20
    -0.15
    -0.10
    -0.05
    0.00
    0.05
    0.10
    0.15
    0.20
    0.25
    0.30
    0.35
    0.40
    0.45
    0.50
    0.55
    0.60
    0.65
    0.70
    0.75
    0.80
    0.85
    0.90
    0.95
    1.00
    1.05
    1.10
    1.15
    1.20
    1.25
    1.30
    1.35
    1.40
    1.45
    1.50
    1.55
    1.60
    1.65
    1.70
    1.75
    1.80
    1.85
    1.90
    1.95
    2.00
    -4
    -2
    0
    2
    -2.5
    -2.4
    -2.3
    -2.2
    -2.1
    -2.0
    -1.9
    -1.8
    -1.7
    -1.6
    -1.5
    -1.4
    -1.3
    -1.2
    -1.1
    -1.0
    -0.9
    -0.8
    -0.7
    -0.6
    -0.5
    -0.4
    -0.3
    -0.2
    -0.1
    0.0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1.0
    1.1
    1.2
    1.3
    1.4
    1.5
    1.6
    1.7
    1.8
    1.9
    2.0
  
  
    x
  
  
    Entries of x vs λ

Content source: emreyamangil/Convex.jl

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