Abstract
Bellman's optimality equation of dynammic programming is examined in the context of a discrete-time, continuous-state economic development model. The main focus of the paper is on the interpretation of this functional equation as a linear programming problem in an infinite-dimensional setting. The connection between this linear programming problem and Bellman's functional equation is developed using a theory of equivalent models. The discrete-state version of the problem is discussed by usual theory for finite-dimensional linear programming. Then the abstract theory for infinite-dimensional linear progTamming is applied to the continuous-state problem in order to obtain results on existence and strong duality, The paper concludes with several simple examples of the dual pair of continuous linear progrmTmling problems.
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