As far as I know after minimization I have to obtain a value $E_{0}\le \frac{\langle \psi (\theta)|H|\psi (\theta)\rangle}{\langle \psi (\theta)|\psi (\theta)\rangle}$, where $E_{0}$ - eigenvalue of ground state for hamiltonian $H$. Sometimes the algorithm give the value close to $E_{0}$, but far more often I get values lower than that.
I use hardwave efficient ansatz for initial state generation.
Hamiltonian consists of Pauli-strings $H=\sum_{ijkl}\sigma_i\sigma_j\sigma_k\sigma_l$.
For parameters optimization I use "COBYLA" and "Nelder-Mead" methods.
Could it be that the ansatz produce a state space which is not large enough?