In the Variational Quantum Linear Solver (VQLS) paper they define four cost functions (2 global and 2 local) and state in Appendix B that "all four cost functions are non-negative." However, in the qiskit VQLS tutorial where they implement one of the global cost functions you can see from their output that the cost function tends to negative numbers (~$-25$). Does this imply that they have an incorrect implementation of the cost function? What does it mean to have a negative cost function?
For some context, I am working with the local cost function, and it sometimes goes negative but not always. The reason I ask these questions is because I am unsure about how to handle convergence for my optimizer for negative cost functions.