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
(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
Once you know a closed form for Q(x, ω ), you just integrate
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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- Spring '08
- Optimization, stochastic programming