Proceedings of the Centre for Mathematics and its Applications

Bellman's equation and a continuous linear programming problem

W.R.S. Sutherland

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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.

Article information

Source
Workshop/Miniconference on Functional Analysis and Optimization. Simon Fitzpatrick and John Giles, eds. Proceedings of the Centre for Mathematical Analysis, v. 20. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1988), 187-194

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416340114

Citation

Sutherland, W.R.S. Bellman's equation and a continuous linear programming problem. Workshop/Miniconference on Functional Analysis and Optimization, 187--194, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1988.https://projecteuclid.org/euclid.pcma/1416340114


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