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I wish to use fmincon to solve a linear optimization problem formulated as : enter image description here

v and at are random parameters approximateb by S scenarios.
p is the parobability of each scenario.
wt,xt,yt,zt,Wm and Ym are the problem variables.

I wonder how to set up the model especially the objective function ?(the parameter p and a are defined elsewhere by a script). I implemented the deterministic formulation of the problem as :

 min f(x) such that :
            Aeq.x = beq
            lb<= x <=ub

Is it the same with the stochastic version?

Thanks.

dinjake
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  • The problem you have posted is a deterministic reformulation of a stochastic program. To be more precise, a stochastic program is the one of the form: `max E[f(x)] subject to g(x) >= 0` (in general); after you've made particular assumptions (you distribution is discrete, etc.), it's easy to write the extended formulation (e.g., you've posted). So, yes, you can solve it with any LP solver since now it's LP. Keep is mind, your LP is structured (sparse), so any decomposition (Benders, Danzig-Wolfe) can make your calculation faster. – serge_k Mar 30 '16 at 06:47
  • Thanks serge_k for the clarification; I'm pretty new to Optimization and barely understand it .i find a difficulty in writing the objective function especially that i'm using a special method to generate the scenarios of my random parameters and estimate their probability (in script file). How can i define this probability in the objfunction file ? then how should i call for it knowing that i'm using fmincon inside a for loop to iterate over random parameter ?. Decomposition techniques are used just for large number of scenarios ? .Thanks again – dinjake Mar 31 '16 at 13:25
  • yes, decomposition techniques are usefull for large number of scenarios; probabilities are estimated before throwing to linear program and usualy are taken as input (technically you need to miltiply two numbers to obtain the objective coefficient for each variable). – serge_k Mar 31 '16 at 13:56

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