I'm having a hard time figuring out to find argmin value for the $x_{k+1}$ value in the dual ascent method.
Dual ascent method is $$ x_{k+1}=\operatorname{argmin} L(x, v_k) $$ $$ v_{k+1} = v_k + a_k(A\cdot x_{k+1} -b) $$
I know that I need to update the x and v value every iteration, but when you compute the argmin L value, do we need to use fmincon for (lagrangian function, xinit, A, b ) value as parameters to get argmin in every iteration? or set x equal to the value from the previous iteration?