On the Robustness of Global Optima and Stationary Solutions to Stochastic Mathematical Programs with Equilibrium Constraints, Part 2: Applications

  • C. Cromvik
  • M. Patriksson


In a companion paper (Cromvik and Patriksson, Part I, J. Optim. Theory Appl., 2010), the mathematical modeling framework SMPEC was studied; in particular, global optima and stationary solutions to SMPECs were shown to be robust with respect to the underlying probability distribution under certain assumptions. Further, the framework and theory were elaborated to cover extensions of the upper-level objective: minimization of the conditional value-at-risk (CVaR) and treatment of the multiobjective case. In this paper, we consider two applications of these results: a classic traffic network design problem, where travel costs are uncertain, and the optimization of a treatment plan in intensity modulated radiation therapy, where the machine parameters and the position of the organs are uncertain. Owing to the generality of SMPEC, we can model these two very different applications within the same framework. Our findings illustrate the large potential in utilizing the SMPEC formalism for modeling and analysis purposes; in particular, information from scenarios in the lower-level problem may provide very useful additional insights into a particular application.

Stochastic mathematical program with equilibrium constraints Solution stability and robustness Traffic network design Intensity modulated radiation therapy Sample average approximation 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Mathematical SciencesChalmers University of Technology and Mathematical Sciences, University of GothenburgGothenburgSweden

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