Optimization problem for ellipse fitting

I'm trying to "A robust ellipse fitting algorithm based on sparsity of outliers, Elaheh Sobhani" with MATLAB.

As I follow this paper, cost function & matrices do not converge but diverge.

Could you check if there's anything missing in the code?

Thx :)

Paper content ===========================================================

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%% data vector setting

data_len = length(data);

X = [];

for i=1:data_len

data_x = data(i,1);

data_y = data(i,2);

x = [];

x = [data_x^2, data_x*data_y, data_y^2, data_x, data_y]';

X = [X,x];

end

X_T = transpose(X);

%% initialize o vector with the zero vector & one vector

o = zeros(data_len,1);

I = ones(data_len,1); %rescaling

lambda = 0.2;

%% Repeat part

loop_cnt = 0;

while true

loop_cnt = loop_cnt + 1;

disp(loop_cnt);

a = ctranspose(X_T)*(o + I);

for i = 1:data_len

o(i) = transpose(X(:,i)) * a - 1 - lambda * sign(o(i));

end

loss = 1/2 * norm( X_T * a - I - o, 2)^2 + lambda * norm(o,1);

if loss < 100

break;

end

end