Matlab Multivariable Minimization - algorithm

Question

I'm trying to develop the adaptive unsharp algorithm described by Polesel et al. in the article "Image Enhancement via Adaptive Unsharp Masking" (link to the article). The core of the algorithm is the minimization of a cost function defined as:
J(m,n) = E[e(m,n)^2] = E[(gd(m,n)-gy(m,n))^2]
where E[] is the statistical expectation and gy(m,n) is:
gy(m,n) = gx(m,n) + lambda1(m,n)*gzx(m,n) + lambda2(m,n)*gzy(m,n);
I want to find lambda1 and lambda2 for each pixel in order to minimize the cost function in each pixel.
Here the code that I wrote so far:
function [ o_sharpened_image ] = AdaptativeUnsharpMask( i_image , t1, t2)
%ADAPTATIVEUNSHARPMASK Summary of this function goes here
% Detailed explanation goes here
if isa(i_image,'dip_image')
i_image = dip_array(i_image);
end
if ~isfloat(i_image)
i_image = im2double(i_image);
end
adh = 4;
adl = 3;
g = [-1 -1 -1; -1 8 -1; -1 -1 -1];
dim = size(i_image);
lambda_x = 0.5*ones(dim);
lambda_y = 0.5*ones(dim);
z_x = conv2(i_image,[-1 2 -1],'same');
z_y = conv2(i_image,[-1; 2; -1],'same');
g_x = conv2(i_image,g,'same');
g_zx = conv2(z_x,g,'same');
g_zy = conv2(z_y,g,'same');
a = ones(dim);
variance_map = colfilt(i_image,[3 3],'sliding',#var);
a(variance_map >= t1 & variance_map < t2) = adh;
a(variance_map >= t2) = adl;
g_d = a.*g_x;
lambda = [lambda_x lambda_y];
lambda0 = lambda;
lambda_min = lsqnonlin(#(lambda) UnsharpCostFunction(lambda,g_d,g_zx,g_zy),lambda0);
o_sharpened_image = i_image + lambda_min(:,1:size(i_image,2)).*z_x + lambda_min(:,size(i_image,2)+1:end).*z_y;
end
Here the code of the cost function:
function [ J ] = UnsharpCostFunction( i_lambda, i_gd, i_gzx, i_gzy )
%UNSHARPCOSTFUNCTION Summary of this function goes herek
gy = i_gd + i_lambda(:,1:size(i_gd,2)).*i_gzx + i_lambda(:,size(i_gd,2)+1:end).*i_gzy;
J = mean((i_gd(:) - gy(:)).^2);
end
For each iteration I print on the command window the value of the J function and it is always the same. What am I doing wrong?
Thank you.