Advanced

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:
author
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
SIAM Publications
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
2007-06-21 14:43:23
date last changed
2017-08-27 03:51:28
@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},
  keyword      = {quasi-convex optimization,convex duality,H$^infty$ space},
  language     = {eng},
  number       = {1},
  pages        = {253--277},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal of Control and Optimization},
  title        = {Duality in $H^infty$ Cone Optimization},
  url          = {http://dx.doi.org/10.1137/S0363012900369617},
  volume       = {41},
  year         = {2002},
}