An informal statement of my problem is as follows:
I have a lagrangian $L1$ defined over a constraint set and my algorithm 'walks' to the saddle point through alternate minimizations and maximations. I call the path the algorithm takes 'Walk1'.
I now shift the inequality constraint that is active in L1 to a new position and walk to the new saddle point of this lagrangian $L2$. The inequality constraint is active here as well. I call this path 'Walk2'.
My question is, is there a way to relate 'walk1' with 'walk2' to the changes in the active constraints ?