## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- 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

### Bellman's equation and a continuous linear programming problem

#### 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

**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