Optimization Method Based On Optimal Control (2309.05280v1)

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.