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Computing optimal control on MATLAB – the SCOM package and economic growth models. (English) Zbl 1002.49001

Rubinov, Alexander (ed.) et al., Optimization and related topics. Selected papers of the 6th Australian optimization day miniconference, Ballarat, Australia, July 16, 1999, and the special sessions on nonlinear dynamics and optimization and operations research - methods and applications, Melbourne, Australia, July 11-15, 1999 (part of the joint meeting of the American Mathematical Society and Australian Mathematical Society). Dordrecht: Kluwer Academic Publishers. Appl. Optim. 47, 61-70 (2001).
Summary: A computer package “SCOM” is described, for solving a class of optimal control problems in continuous time, using the MATLAB system, but in a different way from the “RIOTS\(_-\)95” package which also uses MATLAB. As in the MISER and OCIM packages, the control is parametrized as a step-function, and MATLAB’s “constr” package for constrained optimization is used as a subroutine. End-point conditions are simply handled using penalty terms. Much programming is made unnecessary by the matrix features built into MATLAB. Some economic models present computational difficulties because of implicit constraints, and there is some advantage using finite difference approximations for gradients. The Kendrick-Taylor model of economic growth is computed as an example.
For the entire collection see [Zbl 0974.00048].

MSC:

49-04 Software, source code, etc. for problems pertaining to calculus of variations and optimal control
49M30 Other numerical methods in calculus of variations (MSC2010)
91B62 Economic growth models

Software:

RIOTS_95; Matlab; MISER3; SCOM
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