  Conservation principles like conservation of charge or energy provide a
natural way to couple and constrain different physical variables. In this
letter, we propose a dynamical system model that exploits these constraints for
solving non-convex global optimization problems. Unlike the traditional
simulated annealing or quantum annealing based global optimization techniques,
the proposed method optimizes a target objective function by continuously
evolving a driver functional over a conservation manifold using a generalized
variant of growth transformations. As a result, the driver functional converges
to a Dirac-delta function that is centered at the global optimum of the target
objective function. We provide an outline of the proof of convergence for the
dynamical system model and we demonstrate the application of the model for
implementing linear-time and constant-time decentralized sorting algorithms.
