Minimizing an arbitrary function even without regularization is a hard piece of coding, since you can not apply the same techniques as you can for the convex optimization problems you mentionned (e.g. local extrema, discontinuities etc.).

So, maybe you will have to do some coding yourself with the loss functions you have in mind...

You are right Matthias. But I think there should be a code, at least, for smooth and differentiable functions.

Because of lack of time, writing code is my last plan.

Thank you for your answer.

I found it myself.

This toolbox has some useful functions for minimizing (min_x { f(x) +g(x) }), where both f(x) & g(x) should be continuous and f(x) should be differentiable.

you should provide gradient of f(x) and the proximal of g(x) to toolbox.

when g(x)=||x||1, then proximal of g(x) is a simple soft thresholding function.

http://www.mathworks.com/matlabcentral/fileexchange/file_infos/16204-toolbox-sparse-optmization

Try this:Orthant-Wise Limited-memory Quasi-Newton Optimizer for L1-regularized Objectives(source code available)