how to speed up a large convex problem (10000 variables) by supplying gradient to fmincon

I have a large convex problem that has linear objective function, linear constraints and nonlinear constraints. I put the linear constraints as a matrix and nonlinear constraints in a function. However, it takes a week to run fmincon for 600 iterations (it didnt reach an optimum solution yet). I read that we can speed up fmincon by supplying gradient or hessian to fmincon. But I do not know how to do that. Your help is appreciated

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/268458-provide-gradient-for-fmincon#answer_210053

[mohamed Faraj]

Thank you Walter. Any idea how much time could we save by providing gradient for a large problem?. I am asking because i want to see if it is good to spend time on this.

[Walter Roberson]

If your gradient is dense, then for that kind of size, the numeric estimation that is already done would often be faster, and the controlling factor would be whether you need the additional accuracy possible with the explicit gradient method.

If you gradient is sparse, then there are sparse gradient options that might be useful considering the number of variables.