Global Optimization based on Growth Transform Dynamical Model

TL;DR

This paper introduces a novel dynamical system model leveraging conservation principles to solve non-convex global optimization problems, converging to the global optimum through growth transformations.

Contribution

It presents a new growth transform dynamical model that exploits conservation constraints for efficient global optimization, differing from traditional annealing methods.

Findings

Converges to the global optimum of the target function.

Demonstrates linear-time and constant-time decentralized sorting algorithms.

Provides a convergence proof outline for the proposed dynamical system.

Abstract

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.