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CONSTRAINED OPTIMIZATION OF LINEAR SYSTEMS FOR INFINITE HORIZON PROBLEMS.
CORNELL UNIV ITHACA N Y DEPT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH
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Some methods of optimal control theory are extended with a view toward applications to production and inventory control. A linear, discrete time, deterministic system with vector state and decision variables is optimized relative to a quadratic criterion. The optimal control is shown to be piecewise linear in the state vector when the decision is constrained to be nonnegative, and an algorithm is presented for computing optimal controls. The following results are obtained for the infinite horizon unconstrained problem with no discounting of future costs 1 necessary conditions for convergence of optimal N-period policies. 2 optimal properties of this limit policy. These results are applied to modify the finite horizon algorithm to obtain optimal controls for the infinite horizon constrained problem. Results of some computations are presented. Author
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