Simultaneous Solution Of Families Of Problems

We are interested in a situation where a large number of problems of some common type must be solved. The problems are defined on some space of "solutions", share the same objective function to be optimized, and differ by their sets of constraints. Thus a solution may be feasible with respect to a set of problems and infeasible with respect to the others. We investigate the possibility of solving the problems simultaneously and presenting the optimal solutions compactly, so that each of these solutions can be easily obtained when needed