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Functional equations and successive approximations in linear and nonlinear programming

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  • Richard Bellman

Abstract

The purpose of this paper is to illustrate the applicability of two of the fundamental tools of classical analysis, functional equations and successive approximations, to various classes of multidimensional maximization problems. The advent of the modern digital computer makes it particularly appropriate that this synthesis of new and old be made. Today we can envisage as single steps in an iterative solution the resolution of particular problems which even ten years ago would have been considered as beyond the scope of mathematical power. Since the rules of the game have changed so drastically insofar as what we accept as a feasible solution, it is essential that we revise many of our techniques with this well in mind. Suitably combining classical and modern devices, we can hope to make a start on the solution of the many complex and significant problems that challenge us.

Suggested Citation

  • Richard Bellman, 1960. "Functional equations and successive approximations in linear and nonlinear programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 7(1), pages 63-83, March.
    • Handle: RePEc:wly:navlog:v:7:y:1960:i:1:p:63-83
    DOI: 10.1002/nav.3800070108
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