Way out of my comfort zone here so apologies if I'm not providing enough or correct information. I work with an application of constrained optimization to assemble test forms (automated test assembly). I have an intuitive understanding of the fact that, if there is a feasible solution to a constrained optimization problem with, say, K constraints, that there will also be a feasible solution to the same problem with any subset of those K constraints, but I'm interested in whether there is a formal proof of this. My understanding is that any subset of those K constraints represent a more relaxed problem in a sense, so if the more constrained or difficult problem is solvable then any more relaxed problem nested in that problem is also solvable. (Not necessarily that it produces the same solution -- it's ok for the solution to be different -- just that it's still solvable.) Does anyone know of any formal proofs of this? Or can anyone point me toward any reading that discusses this? I have a background in applied statistics and educational psychology but will do my best to digest the more complex math that I am almost certain (with dread) this will entail. :)
Thanks!