| Bellman最优性原理——论动态规划(Ⅰ) |
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| 引用本文： | 秦裕瑗.Bellman最优性原理——论动态规划(Ⅰ)[J].应用数学,1994(3). |
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| 作者姓名： | 秦裕瑗 |
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| 作者单位： | 武汉钢铁学院 430081 |
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| 摘 要： | 对于Bellman最优性原理,本文举出实例表明:(1)策略不一定有(合理的)子策略;(2)子策略不一定存在最优子策略;(3)最优策略不一定有最优子策略;(4)用最短路与反证法来论述最优性原理的正确性,不能肯定成立;(5)Bellman最优性原理与其递推公式并不等价。 讨论四类最优策略之后,给出最优性原理与递推公式等价的一个充分性定理。
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| 关 键 词： | 策略 强优选半域 最优性原理 四类最优策略 |
Bellman's Principle of Optimality -On Dynamic Programming ( I ) |
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| Qin Yuyuan.Bellman's Principle of Optimality -On Dynamic Programming ( I )[J].Mathematica Applicata,1994(3). |
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| Authors: | Qin Yuyuan |
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| Institution: | Wuhan Iron and Steel University 430081 |
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| Abstract: | Belllman' s principle of optimality is the basis of optimization problems in multistage di-cision systems. It gives several examples to show that (i) policies need not have (reasonable) sub-policies; (ii) a system has optimum policies,its sub-system need not have;(iii) optimum policies need not have optimum sub-policies; (iv) the reasoning for the principle by prpof-by-contradiction is not necessarily true;(v) the principle and related recursive formula need not be equivalent.
After discussing four kinds of optimum path problems, it proves a sufficient condition for the equivalence of the principle and the recursive formula. |
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| Keywords: | Policy Strongly optimizing semi-field Principle of optirnality Four kinds of optimum policy |
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