Modern methods for solving the optimal control problem in economics

Abstract

The modern formulation of the optimal control problem is given, following which a survey of the methods currently applied in solving the optimal control problem in economics is conducted, with a focus given to numerical methods. The most important problems in the application of numerical methods in solving the optimal control problem are given and explained. The article then lists and explains the most common computational methods of solving the optimal control problem that are being applied in todays economic sphere, how far these methods go in terms of achieving their objectives and providing solutions, the difficulties in implementing these methods, and the associated limitations. The latest developments in software and programs that are beginning to be used by mainly economists in solving some of the most common optimal control problems are listed, and their advantages and limitations are explained. Lastly, a general analysis of some of the next-generation methods and the future of the optimal control problem in general is made.