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hw3 - Stochastic Programming Homework 3 UFID 5114-0690 Name...

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Stochastic Programming Homework 3 UFID: 5114-0690 Name: Shuang Chen Problem 1: a) Q ( x, ξ ) = min y { 2 y 1 + y 2 | y 1 + 2 y 1 ξ 1 - x 1 , y 1 + y 2 ξ 2 - x 1 - x 2 , 0 y 1 1 , 0 y 2 1 } K 2 ( ξ ) = { x | Q ( x, ξ ) < + ∞} , Combine the above equations, we can obtain that: K 2 ( ξ ) = { x | x 1 ξ 1 - 3 , x 1 + x 2 ξ 2 - 2 } . b) 1) By the fact that ξ 1 , ξ 2 both have uniform density over [2 , 4], we can deduce that ξ 1 - 3 [ - 1 , 1] and ξ 2 - 2 [0 , 2], in addition, because K p 2 = intersectiontext ξ Ξ K 2 ( ξ ), we find out K p 2 = { x | x 1 1 , x 1 + x 2 2 } 2) Because in our case Ξ is finite, K p 2 coincides with
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