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。
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.
出处
《应用数学》
CSCD
北大核心
1994年第3期349-354,共6页
Mathematica Applicata
关键词
最优性原理
贝尔曼最优性
动态规则
Policy
Strongly optimizing semi-field
Principle of optirnality
Four kinds of optimum policy.
