Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

Abstract

AbstractImproving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation (CNOP), which has been applied widely in predictability studies. In this study, the Differential Evolution (DE) algorithm, which is a derivative-free algorithm and has been applied to obtain CNOPs for exploring the uncertainty of terrestrial ecosystem processes, was employed to obtain the CNOPs for finite-dimensional optimization problems with ball constraint conditions using Burgers’ equation. The aim was first to test if the CNOP calculated by the DE algorithm is similar to that computed by traditional optimization algorithms, such as the Spectral Projected Gradient (SPG2) algorithm. The second motive was to supply a possible route through which the CNOP approach can be applied in predictability studies in the atmospheric and oceanic sciences without obtaining a model adjoint system, or f...