Let be the value function for the dynamic programming problem (example 2.32). Assume that ¢ f is
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be the value function for the dynamic programming problem (example 2.32). Assume that
¢ f is bounded on X Ã X
¢ G(x) is nonempty for every x X
Show that the plan x* = (x0, x*1, x*2, ...) Î (x0) is optimal if and only if it satisfies Bellman's equation
v(x*1) = f(x*t , x*t+1) + βv(x*t+1), t = 0, 1, 2,... (13)
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