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lecture14

# For example if min qx 3 qx df march

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Unformatted text preview: really is a multidimensional integral. • For example, if Ω ⊆ 3 , ∞ ∞ ∞ min Q(x) = Q(x, ω )dF (ω ) −∞ March 3, 2003 −∞ −∞ Stochastic Programming  Lecture 14 Slide 4 Scary Looking! min cT x + x∈X ··· Q(x, ω ) Ω • Who knows how to solve optimization problems with integrals in them? (NOT ME!) • It is even very dif cult to evaluate the function that you are trying to optimize. • Things you can try... • 1. Solve the distribution problem. March 3, 2003 Stochastic Programming  Lecture 14 Slide 5 The Distribution Problem • Develop a closed form expression for Q(x, ω ) You obtain a solution to the recourse problem (for any value of x and realization ω ) by inspection. You have done this (or something similar) in HW#1, and HW#2. Once you know a closed form for Q(x, ω ), you just integrate away... It is possible to obtain a closed form Q(x, ω ) only for very simple problems. March 3, 2003 Stochastic Programming  Lecture 14 Slide 6 March 3, 2003 Stochastic Programming  Lecture 1...
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