Dual mean field annealing scheme for binary optimization under linear constraints

It is shown that certain general classes of constrained binary optimization tasks can be solved with increasing accuracy by a first order mean field approximation of the Boltzmann distribution of the associated Lagrangian as the instance size grows. The formalism is thoroughly analyzed for the quadratic and multidimensional knapsack models. In these cases analytical expressions for the convergence of the optimality gaps are given, which are experimentally verified.