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Duality in $H^infty$ Cone Optimization

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Author

Summary, in English

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.

Publishing year

2002

Language

English

Pages

253-277

Publication/Series

SIAM Journal of Control and Optimization

Volume

41

Issue

1

Document type

Journal article

Publisher

Society for Industrial and Applied Mathematics

Topic

  • Control Engineering

Keywords

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

Status

Published

ISBN/ISSN/Other

  • ISSN: 1095-7138