# Examples of problems that cannot be formulated as optimization problems

An optimization problem has 3 main components: decision variables, constraints and an objective function. Such a problem can be mathematically modelled and solved using an optimization solver. For example, a SUDOKU puzzle can be modelled as such and solved using a solver.

What are examples of famous real-life problems or puzzles that cannot be modelled as optimization problems? I reviewed relevant literature, but could not find any discussion on problems that cannot be modelled as optimization problems.

If you are allowed to assume that an objective function can mean a boolean function that is true if and only if the found solution satisfies the given constraints (rules of the puzzle), – then any mathematical problem can be formulated in such a way.