which algorithm to use for my own structured sparse coding problem?

I want to solve a sparse coding problem which have extra terms in its optimization problem. For example constraint (or objective term) on the 2nd derivative of Dictionary elements, or additional constraint on the coefficients to lock some of them together as they'd update in a similar way.

I noticed there are a number of available algorithms like NMF, KSVD, MP and maybe more. But i'm not sure which algorithm to choose to solve my problem.

- I also prefer the coefficients to be non-negative (so maybe someone suggest NMF!) and i like to design an online algorithm to be able to update the dictionary with new samples of data.

Looking forward to hear your suggestions :)