Decentralized Global Optimization Based on a Growth Transform Dynamical System Model

Conservation principles, such as conservation of charge, energy, or mass, provide a natural way to couple and constrain spatially separated variables. In this paper, we propose a dynamical system model that exploits these constraints for solving nonconvex and discrete 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 asymptotically converges toward a Dirac-delta function that is centered at the global optimum of the target objective function. In this paper, we provide an outline of the proof of convergence for the dynamical system model and investigate different properties of the model using a benchmark nonlinear optimization problem. Also, we demonstrate how a discrete variant of the proposed dynamical system can be used for implementing decentralized optimization algorithms, where an ensemble of spatially separated entities (for example, biological cells or simple computational units) can collectively implement specific functions, such as winner-take-all and ranking, by exchanging signals only with its immediate substrate or environment. The proposed dynamical system model could potentially be used to implement continuous-time optimizers, annealers, and neural networks.