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Dual Problem in Multi-Objective Hp Control

Ghulchak, Andrey LU (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:
author
organization
publishing date
type
Contribution to conference
publication status
published
subject
keywords
multiple objectives, convex duality, linear system
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
2007-09-18 09:20:23
date last changed
2016-04-16 12:18:23
@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},
  keyword      = {multiple objectives,convex duality,linear system},
  language     = {eng},
  title        = {Dual Problem in Multi-Objective Hp Control},
  year         = {2001},
}