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On the robustness of global optima and stationary solutions to stochastic mathematical programs with equilibrium constraints. II: Applications. (English) Zbl 1201.90140

For stochastic mathematical programs with equilibrium constraints (SMPEC) stability with respect to changes in the underlying probability distribution was studied in the accompanying paper [C. Cromvik and M. Patriksson, J. Optim. Theory Appl. 144, No. 3, 461–478 (2010; Zbl 1201.90139)]. Two applications of theoretical results are presented: a classic traffic network design problem, where the travel costs are uncertain, and the optimization of a treatment plan in intensity modulated radiation therapy, where the machine parameters and the position of organs are uncertain. The sample average approximation method is exploited to solve these problems numerically.

MSC:

90C15 Stochastic programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Citations:

Zbl 1201.90139

Software:

CERR; SNOPT; GALAHAD
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Full Text: DOI

References:

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