It is demonstrated that the method of simulated annealing can be successfully used for constructing an algorithm for solving the self-consistent field or the more general multi-configuration self-consistent field problems. It is shown that the simulated annealing based calculations do not encounter any difficulty even when a pathological divergence cripples a first-order MC SCF method. Applicability of the simulated annealing based strategy in solving general nonlinear matrix equations even in the presence of strong coupling is demonstrated in a model problem.