The advantage of symplectic Euler in optimization and its application

Abstract

Many professions today place a high value on optimization, and many problems can eventually be transformed into optimization issues. There are many iterative methods available today to handle optimization issues, however many algorithms' design principles are unclear. Weijie Su solved this problem by discretizing the iterative equation using an ordinary differential equation, but different discretization techniques will provide different outcomes. So choosing an appropriate method is important. Three discretization techniquesexplicit Euler, implicit Euler, and symplectic Eulerare compared in this work. It is found that while both symplectic and implicit Euler can accelerate the process, only symplectic Euler can be put to use in practice. This further demonstrates symplectic Euler's supremacy in iteration. The use of symplectic Euler in other fields is also introduced in this study, particularly in the Lotka-Volterra equation where promising results might be attained. Symplectic Euler is critical to optimization and is likely to be applied in more areas in the future.