Matlab solver for unconstrained convex optimization

I have a large scale unconstrained convex optimization problem as follows

min , where and u are N-dimensional vectors, λ is a scalar. They are all provided before optimization. Here, M and N are very large.

I use fminunc function in matlab, but it is too slow. Does matlab have some accelerated solver for the above unconstrained convex optimization?

Answer 1

[John D'Errico]

Everybody wants things to be incredibly fast. Large problems can take large time.

Nothing stops you from writing a simple gradient descent solver. Put a line search on it. Will it work well? Who knows.

https://www.ruder.io/optimizing-gradient-descent/

In fact, I see that fminunc can perform a simple gradient descent scheme.

https://www.mathworks.com/matlabcentral/answers/424002-is-there-any-gradient-descent-method-available

In there, we see the flag to cause fminunc to use gradient descent.

https://www.mathworks.com/help/optim/ug/banana-function-minimization.html

Finally, if the objective function is as simple as you show, then you will probably gain by providing the Jacobian yourself, instead of letting it compute the gradient using a finite difference.