Why would we appreciate unsolvable problems?
If an optimization problem doesn't have a solution, does that mean optimization to that degree (i.e. such lowest/highest value) is impossible and we simply do not consider such cases?
These examples are extremely reminiscent of linear programming. Is there any place where an LP solver can be used in graphics, or are the functions always nonlinear?
How does a general-purpose solver determine whether a problem has a solution?
Is there an efficient method to determine whether such a solution exists?
If so many "simple" constraints are infeasible, how are we able to do much more complicated optimizations? Do they just happen to work out?
How would we deal with unsolvable problems?