Does the situation in optimization ever occur in which you have a problem whose feasible set is not described in terms of explicit algebraic equations, but instead you have a large set of points that roughly approximates the feasible set? If so, is there a term for this?
In my particular case I have a large set of samples that I know to be feasible, and the natural thing to do is surround them with balls of some fixed radius, and then use their union as my feasible set. I'd like to know if this is delving into some well-studied area of optimization.