A minimizing principle for the Poisson-Boltzmann equation

TL;DR

This paper introduces a convex dual functional for the Poisson-Boltzmann equation, enabling more effective local optimization by overcoming the non-convexity of the traditional variational formulation.

Contribution

It presents a novel convex dual formulation of the Poisson-Boltzmann equation, improving the applicability of variational methods in coupled dynamic systems.

Findings

The dual functional is numerically equivalent to the original at its minimum.

The convex dual enables local optimization techniques to be effectively applied.

The approach improves the stability and efficiency of solving the Poisson-Boltzmann equation.

Abstract

The Poisson-Boltzmann equation is often presented via a variational formulation based on the electrostatic potential. However, the functional has the defect of being non-convex. It can not be used as a local minimization principle while coupled to other dynamic degrees of freedom. We formulate a convex dual functional which is numerically equivalent at its minimum and which is more suited to local optimization.