An infrared antireflection (AR) coating for germanium is taken as an example to numerically analyze the performance of the local optimization algorithm which is based on Matlab optimization toolbox in the local optimal design of multilayer optical coatings and their application feasibility in the algorithm development of reverse engineering of multilayer optical coatings. The reasons and the solutions of the mutiple solutions in numerical experiments are discussed. The numerical optimization results show that the derivative algorithms of Matlab optimization toolbox have better local optimum point search ability and converging speed than reference methods. While the performance of non-derivative algorithms is poor but might be applicable in the initial local design stage to explore more search directions. In the reverse engineering of multilayer optical coatings, the algorithm lsqnonlin and fsolve are excellent in inversion which determines the quality of optical structural parameters. They are recommended to be the main reverse engineering algorithms. The fminunc and fmincon algorithms can be chosen as supplementary reverse engineering algorithms for their acceptable reverse determination effectiveness. The fminimax and other non-derivative algorithms are poor in effectiveness and stochastic in final solutions, which can easily converge to wrong structural parameters and could not be used as reverse engineering algorithms.