Typo in doc?

[fabianp]

The documentation for DR2_TV states that it solves a problem of the form

min_w gam(f_1(w)+f_2(w)) + 0.5*norm(w)^2 -u^w

Is this a typo and it should read min_w gam(f_1(w)+f_2(w)) + 0.5*norm(w - u)^2 ?

[fabianp]

In particular I don't understand what does u^w mean in the original formula

[albarji]

Hi @fabianp , my apologies for the late reply.

There is indeed a typo: the optimization problem should read

min_w gam(f_1(w)+f_2(w)) + 0.5*norm(w)^2 - u · w

the last term being the inner product of vectors u and w. This is nothing but a shifted version of 2-dimensional TV: if you complete the square using the two last terms you would get

min_w gam(f_1(w)+f_2(w)) + 0.5*norm(w-u)^2 - 0.5*norm(u)

and you can drop the last (constant) term, obtaining the original 2-dimensional TV problem.