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Duality in $H^infty$ Cone Optimization

Ghulchak, Andrey LU and Rantzer, Anders LU (2002) In SIAM Journal of Control and Optimization 41(1). p.253-277
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.
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
quasi-convex optimization, convex duality, H$^infty$ space
in
SIAM Journal of Control and Optimization
volume
41
issue
1
pages
253 - 277
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • wos:000176312200011
  • scopus:0037227329
ISSN
1095-7138
DOI
10.1137/S0363012900369617
language
English
LU publication?
yes
id
be7148e2-689f-48ac-91ea-79bba1472e9f (old id 161983)
date added to LUP
2016-04-01 11:43:32
date last changed
2022-01-26 17:17:42
@article{be7148e2-689f-48ac-91ea-79bba1472e9f,
  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.}},
  author       = {{Ghulchak, Andrey and Rantzer, Anders}},
  issn         = {{1095-7138}},
  keywords     = {{quasi-convex optimization; convex duality; H$^infty$ space}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{253--277}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{SIAM Journal of Control and Optimization}},
  title        = {{Duality in $H^infty$ Cone Optimization}},
  url          = {{http://dx.doi.org/10.1137/S0363012900369617}},
  doi          = {{10.1137/S0363012900369617}},
  volume       = {{41}},
  year         = {{2002}},
}