An explicit linear solution for the quadratic dynamic programming problem |
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| Authors: | W. R. S. Sutherland H. Wolkowicz V. Zeidan |
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| Affiliation: | (1) Department of Mathematics, Statistics and Computing Sciences, Dalhousie University, Halifax, Nova Scotia, Canada;(2) Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada;(3) Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada |
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| Abstract: | For a given vectorx0, the sequence {xt} which optimizes the sum of discounted rewardsr(xt, xt+1), wherer is a quadratic function, is shown to be generated by a linear decision rulext+1=Sxt+R. Moreover, the coefficientsR,S are given by explicit formulas in terms of the coefficients of the reward functionr. A unique steady-state is shown to exist (except for a degenerate case), and its stability is discussed. |
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| Keywords: | Dynamic programming discrete-time control theory linear decision rules |
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