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Unformatted text preview: μ ε for value V ( s, x ). Then, one divides the sum over [ s, T − 1] into segments over [ s, t − 1] and [ t, T − 1]. The cost over [ t, T ] with this controller is certainly higher than the value given initial time t and the state at that time. 3. (5) Let f 1 , f 2 be convex functions mapping IR n into IR . Let g . = f 1 ⊕ f 2 . That is, let g ( x ) = f 1 ( x ) ⊕ f 2 ( x ) = max { f 1 ( x ) , f 2 ( x ) } for all x ∈ IR n . Prove that g is convex. 1 4. (5) Suppose f : IR → IR is convex. Let ¯ x ∈ argmin { f } . Is f monotonically increasing on [¯ x, ∞ )? If so, prove it. If not, provide a counterexample. 2...
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 Spring '08
 Mceneaney,W
 MAE 288A Assignment, discretetime stochastic control, covariance matrix Q.

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