Solving semi-infinite optimization problems with interior point techniques

Oliver Stein, Georg J. Still

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67 Citations (Scopus)
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We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads to central path conditions for the lower level problems, where for a given path parameter a smooth nonlinear finite optimization problem has to be solved. The solution of the semi-infinite optimization problem then amounts to driving the path parameter to zero. We show convergence properties of the method and give a number of numerical examples from design centering and from robust optimization, where actually so-called generalized semi-infinite optimization problems are solved. The presented method is easy to implement, and in our examples it works well for dimensions of the semi-infinite index set at least up to 150.
Original languageEnglish
Pages (from-to)769-788
Number of pages20
JournalSIAM journal on control and optimization
Issue number3
Publication statusPublished - 2003


  • Generalized semi-infinite optimization
  • Convexity
  • Stackelberg game
  • Nonlinear complementarity problem function
  • Smoothing
  • Optimality conditions


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