How to minimize this function using BFGS algorithm?

Let Y(x,t)={y1(x,t),y2(x,t),y3(x,t)} a vector of value define at some nodes x where 1<=x<=100 and this vector varie on time t.

we search to minimize the cost function J(Y(x,0)) with respect to Y(x,0).

The problem is this function is calculated numericaly and has a value at each increment of time so we have for exemple :

t=0 | J(Y(x,0))=1.2 ;

t=0.1 | J(Y(x,0))=2.3;

.

..;

t=1 | J(Y(x,0))=1.0;

and so on ...

We have also calculated the gradient of J numerically (a vector) and we have its value at each increment of time t:

J'(t)={val1(t),val2(t),val3(t)}.

Is it possible to minimize this function ??

Thank's for your help