I am working on this constrained optimization problem. The objective function is the efficiency of the machine which is determined by 6 controllable variables. The constraint is the pressure can't exceed 10 psi. The pressure is dependent on a set of unknown parameters which most likely has little overlap with the 6 controllable variables.
In a nutshell
Objective function f(X)
Constraints g(Y) < 10
Typical optimization problem usually has the same parameters for objective function and constraint. What should I do if objective and constaints are using different sets of variables?
If it is truly the case that your objective function depends on a vector X, and your constraints depend on a vector Y, and there is no relationship between values of Y and values of X, then the constraints are irrelevant, and your problem is an unconstrained optimization problem.
My guess is that there is a relationship, and you just have to write out the math to know what that relationship is.
If you dont know about the relationship between variables and responses, try using a designed experiment. If you have 6 parameters to test, you could use a definitive screening design. Use PSI and your other response in your model, then do a multi-objective function optimization.