Optimization Method Based On Optimal Control

TL;DR

This paper introduces an optimization method based on optimal control theory, utilizing Pontryagin's Maximum Principle to iteratively find solutions with high precision and low oscillation, suitable for non-convex functions.

Contribution

The paper develops a novel optimization approach by transforming problems into optimal control and deriving iterative update gains using FBDEs.

Findings

High precision in solutions

Low oscillation during convergence

Effective in finding local minima of non-convex functions

Abstract

In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal control by designing an appropriate cost function. Using Pontryagin's Maximum Principle and the associated forward-backward difference equations (FBDEs), we derive the iterative update gain for the optimization. The steady system state can be considered as the solution to the optimization problem. Finally, we discuss the compelling characteristics of our method and further demonstrate its high precision, low oscillation, and applicability for finding different local minima of non-convex functions through several simulation examples.