Mean field annealing: a formalism for constructing GNC-like algorithms

Optimization problems are approached using mean field annealing (MFA), which is a deterministic approximation, using mean field theory and based on Peierls´s inequality, to simulated annealing. The MFA mathematics are applied to three different objective function examples. In each case, MFA produces a minimization algorithm that is a type of graduated nonconvexity. When applied to the `weak-membrane´ objective, MFA results in an algorithm qualitatively identical to the published GNC algorithm. One of the examples, MFA applied to a piecewise-constant objective function, is then compared experimentally with the corresponding GNC weak-membrane algorithm. The mathematics of MFA are shown to provide a powerful and general tool for deriving optimization algorithms