Dual Problem in Multi-Objective Hp Control
(2001)- Abstract
- In this paper, we approach a multiobjective Hp prob
lem with several Hp constraints from the Banach
duality point of view. The problem is reduced to an
abstract norm minimization problem, and the dual
problem is derived using the classical Banach re
sult. It completes the primaldual pair which can
be used to solve the problem numerically by nite
dimensional approximations. While the approxima
tion of the primal problem gives an upper bound
of the optimal value, the approximation of the dual
problem provides a lower bound, and the gap be
tween them can be done arbitrary small. In view of
growing computational power of modern... (More) - In this paper, we approach a multiobjective Hp prob
lem with several Hp constraints from the Banach
duality point of view. The problem is reduced to an
abstract norm minimization problem, and the dual
problem is derived using the classical Banach re
sult. It completes the primaldual pair which can
be used to solve the problem numerically by nite
dimensional approximations. While the approxima
tion of the primal problem gives an upper bound
of the optimal value, the approximation of the dual
problem provides a lower bound, and the gap be
tween them can be done arbitrary small. In view of
growing computational power of modern computers,
it gives a good alternative to the standard mixed
objective approach. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/537877
- author
- Ghulchak, Andrey LU
- organization
- publishing date
- 2001
- type
- Contribution to conference
- publication status
- published
- subject
- keywords
- multiple objectives, convex duality, linear system
- external identifiers
-
- scopus:84947466299
- language
- English
- LU publication?
- yes
- id
- 4ab25812-2c97-4564-aa48-d1c5410920b8 (old id 537877)
- alternative location
- http://citeseer.ist.psu.edu/449445.html
- date added to LUP
- 2016-04-04 14:15:40
- date last changed
- 2022-01-30 01:44:51
@misc{4ab25812-2c97-4564-aa48-d1c5410920b8, abstract = {{In this paper, we approach a multiobjective Hp prob<br/><br> lem with several Hp constraints from the Banach<br/><br> duality point of view. The problem is reduced to an<br/><br> abstract norm minimization problem, and the dual<br/><br> problem is derived using the classical Banach re<br/><br> sult. It completes the primaldual pair which can<br/><br> be used to solve the problem numerically by nite<br/><br> dimensional approximations. While the approxima<br/><br> tion of the primal problem gives an upper bound<br/><br> of the optimal value, the approximation of the dual<br/><br> problem provides a lower bound, and the gap be<br/><br> tween them can be done arbitrary small. In view of<br/><br> growing computational power of modern computers,<br/><br> it gives a good alternative to the standard mixed<br/><br> objective approach.}}, author = {{Ghulchak, Andrey}}, keywords = {{multiple objectives; convex duality; linear system}}, language = {{eng}}, title = {{Dual Problem in Multi-Objective Hp Control}}, url = {{https://lup.lub.lu.se/search/files/6318771/625716.pdf}}, year = {{2001}}, }