optimization, Bosted difference of convex functions algorithm, Mathematics

Hello dear freinds,

I wish to get help for my code here. I am coding an algorithm, that called BDCA which is an improvment of the DCA. The first algorithm should improve the first one, but this is not happend in my code and I do not know why.

The algorithm is

Taking x_{0} as any initial condition and k=0. Fix \alpha >0 and \beta \in (0,1) \\

Select s_{k}\in \partial g(x_{k}) and compute y_k by solving (1)

\underset{x\in \mathbb{R}^n}{\min} \quad \phi_{k}(x):= f(x) - (g(x^2_{k})+s^T_{k}(x^2-x^2_{k})).

Set d_{k,i}= 0, if, y_{k,i}=0, \\ else, d_{k,i}= \frac{y^2_{k,i}-x^2_{k,i}}{2y_{k,i}} &

If $d_{k,i}=0$ : Stop and return $x_{k}$. Otherwise go to the next step.

Compute stepsize t_{k}:=\max \{\beta^l | l=0,1,2...\} s.t.

\phi(y_{k}+t_{k}d_{k})\leq \phi(y_{k})-\alpha t^2_{k}{\lVert d_{k}\rVert}^2\\

Set x_{k+1}=y_{k}+t_{k}d_{k},\\

\State k \gets k+1 and go to 1.

I hope that the algorithm is understanadable, so this Alg has a line search to improve the DCA mentioned before, but I am still getting exactly the same result. I hope some code tell me what I am doing wrong in the following code:

for i=1:N

if u(i)==0

d(i)=0;

else

d(i)=((u(i)^2)-(u_old(i)^2))/(2*u(i));

end

end

if sum(abs(d))==0

u=u_old;

break

else

phi_u=@(u)1/2*(u'*M*u)-(transpose(B)*u)+sum_g(u);

t=1;

while phi_u(u+t*d) > phi_u(u) - alpha *(t^2)* power ( norm (d), 2)

t=0.5*t;

%if t < 1*e -30 % No decrease found

if t < 0.001 % No decrease found

break ;

end

u_k=u+t*d;

if u_old==u_k

u = u_old;

break

else

u_old=u_k;

end

end

end