Duality in $H^infty$ Cone Optimization

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Abstract

Positive real cones in the space $H^infty$ appear naturally in many optimization problems of control theory and signal processing. Although such problems can be solved by finite-dimensional approximations (e.g., Ritz projection), all such approximations are conservative, providing one-sided bounds for the optimal value. In order to obtain both upper and lower bounds of the optimal value, a dual problem approach is developed in this paper. A finite-dimensional approximation of the dual problem gives the opposite bound for the optimal value. Thus, by combining the primal and dual problems, a suboptimal solution to the original problem can be found with any required accuracy.
Original languageEnglish
Pages (from-to)253-277
JournalSIAM Journal of Control and Optimization
Volume41
Issue number1
DOIs
Publication statusPublished - 2002

Subject classification (UKÄ)

  • Control Engineering

Keywords

  • quasi-convex optimization
  • convex duality
  • H$^infty$ space

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