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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/161983
- author
- Ghulchak, Andrey
LU
and Rantzer, Anders
LU
- organization
- publishing date
- 2002
- 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
- 2023-09-01 04:52:52
@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}},
}