  Recently several gain-dissipative platforms based on the networks of optical
parametric oscillators, lasers, and various non-equilibrium Bose-Einstein
condensates have been proposed and realised as analogue Hamiltonian simulators
for solving large-scale hard optimisation problems. However, in these
realisations the parameters of the problem depend on the node occupancies that
are not known a priori, which limits the applicability of the gain-dissipative
simulators to the classes of problems easily solvable by classical
computations. We show how to overcome this difficulty and formulate the
principles of operation of such simulators for solving the NP-hard large-scale
optimisation problems such as constant modulus continuous quadratic
optimisation and quadratic binary optimisation for any general matrix. To solve
such problems any gain-dissipative simulator has to implement a feedback
mechanism for the dynamical adjustment of the gain and coupling strengths.
