WIAS Preprint No. 1785, (2013)

A mixed-integer stochastic nonlinear optimization problem with joint probabilistic constraints


  • Arnold, Thomas
  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Möller, Andris
  • Vigerske, Stefan

2010 Mathematics Subject Classification

  • 90B05 90C15 90C10


  • stochastic optimization, probabilistic constraints, mixed-integer nonlinear programming, power management




We illustrate the solution of a mixed-integer stochastic nonlinear optimization problem in an application of power management. In this application, a coupled system consisting of a hydro power station and a wind farm is considered. The objective is to satisfy the local energy demand and sell any surplus energy on a spot market for a short time horizon. Generation of wind energy is assumed to be random, so that demand satisfaction is modeled by a joint probabilistic constraint taking into account the multivariate distribution. The turbine is forced to either operate between given positive limits or to be shut down. This introduces additional binary decisions. The numerical solution procedure is presented and results are illustrated.

Appeared in

  • Pac. J. Optim., 10 (2014) pp. 5--20.

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