Foundations of Deterministic Optimization Theory |
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assume axiom is satisfied B-space bijection C₁ Chapter compact space concrete control system consider contradiction CORNELL LIBRARY LIBRARY CORNELL UNIVERSITY Corollary corresponding p-topology countably compact D.P.P. which satisfies define Definition 12 denote dynamic programming problems elements Example ɛ g(u F is p-bijective finite following axiom following properties given Grundy function implies induced inf B₂ interval topology isomorphic knapsack problem Lemma let a,b let F Let x,y mapping max P,U memoryless metric space nonempty set Notation open covering optimal policy optimization problems optimizing sequence p-connected p-injective P₁ P₂ preference preordered set Proof properties are equivalent Proposition relative topology result follows result is proven satisfies D.P.10 second countable sequential set P(t subproblem subsets sup B₁ Suppose t₁ t₁,b Theorem total order totally ordered set totally preordered trivial UNIV UNIVERSITY CORNELL UNIVERSITY UNIVERSITY πε χε χερ