What is the optimality argument in a simultaneous column and row generation procedure? By column and row generation procedure I mean a procedure in which every time a column in generated, several constraints need to be added to the master program.
As you are probably aware of, the standard optimality condition for column generation is not valid if not all constraints are included in the master problem, as the dual information of the missing constraints needs to be taken into account in the computation of the reduced costs. Muter et al. (2013) consider this issue and show that if the formulation satisfies certain assumptions, it is possible to anticipate the optimal dual variables of the missing dual variables, such that the reduced costs can be computed correctly.
There are successful applications of this approach, see e.g. this paper or this paper. However, whether this approach is computationally feasible fully depends on your model. In some cases, the pricing problem itself becomes an integer program with exponentially many variables, so then it might be worthwhile to try and come up with a different formulation without column-dependent rows.