Matlab solver for unconstrained convex optimization

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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?

Accepted Answer

John D'Errico
John D'Errico on 2 Dec 2023
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.
In fact, I see that fminunc can perform a simple gradient descent scheme.
In there, we see the flag to cause fminunc to use gradient descent.
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.

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