A simple approach to global optimal feedback solutions : with emphasize on certain management problems in economics

Abstract

Dynamic optimization problems covers a great class of problems in management science and technology. The classical problem formulations being the variational approach as in classical mechanics, like Hamilton's principle and the optimal control theory in economics as the Pontryagin's maximum principle. In this account we start with a general problem formulation as an alternative to an approach based on solving differential equations. We focus on creating an analytical environment aimed at deriving global bounds and approximations. Alternative sufficient and necessary conditions for global optimal solutions are formulated and practical schemes for finding concrete solutions are presented. Optimization problems in a general setting is discussed and we define some ways to extend the problem and approximate solutions. In most of our work we restrict ourselves to problems in the setting of dynamic systems in continuous time. The Principle of Extension is outlined and we also discuss the classical formulations, i.e. The Hamiltonian and Dynamic programming formulations, in the present context. Practical application of the theory is presented as well as a summary and discussion of results.