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In the first and second model, X and Y are supposed to be nonnegative. |
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In mathematics, '''robust optimization''' is an approach in [[optimization (mathematics)|optimization]] to deal with uncertainty. It is similar to the recourse model of [[stochastic programming]], in that some of the parameters are [[random variable]]s, except that feasibility for all possible realizations (called scenarios) is replaced by a [[penalty function]] in the objective. As such, the approach integrates [[goal programming]] with a scenario-based description of problem data. To illustrate, consider the LP:
:<math>\min cx + dy: Ax=b, Bx + Cy = e, x, y \
where d, B, C and e are random variables with possible realizations <math>{(d(s), B(s), C(s), e(s): s \in \{1,...,N\})}</math>, where N = the number of scenarios. The robust optimization model for this LP is:
:<math>\min f(x, y(1), ..., y(N)) + wP(z(1), ..., z(N)): Ax=b, x \
:<math>\ B(s)x + C(s)y(s) + z(s) = e(s),</math> and <math>y(s) \ge 0,\, \forall s = 1,...,N,</math>
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