Rational optimization using sum-of-squares techniques

Motivated by many control applications, this paper deals with the global solutions of unconstrained optimization problems. First, a simple SOS method is presented to find the infimum of a polynomial, which can be handled efficiently using the relevant software tools. The main idea of this method is...

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Bibliographic Details
Main Authors: Lavaei, J., Sojoudi, S., Aghdam, A.G.
Format: Conference Proceeding
Language:English
Subjects:
Application software
Constraint optimization
Java
Nonlinear systems
Output feedback
Polynomials
Robust stability
Robustness
Software tools
USA Councils
Online Access:Request full text
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Summary:Motivated by many control applications, this paper deals with the global solutions of unconstrained optimization problems. First, a simple SOS method is presented to find the infimum of a polynomial, which can be handled efficiently using the relevant software tools. The main idea of this method is to introduce a perturbation variable whose approaching to zero results in a solution with any arbitrary precision. The proposed technique is then extended to the case of rational functions. The primary advantages of this approach over the existing ones are its simplicity and capability of treating problems for which the existing methods are not efficient, as demonstrated in three numerical examples.
ISSN:0191-2216
DOI:10.1109/CDC.2007.4434948