DMCA
Semidefinite Programming Relaxations for Semialgebraic Problems (2001)
Cached
Download Links
- [control.ee.ethz.ch]
- [www.cds.caltech.edu]
- [www.math.uni-klu.ac.at]
- [www.mit.edu]
- DBLP
Other Repositories/Bibliography
| Citations: | 361 - 23 self |
BibTeX
@MISC{Parrilo01semidefiniteprogramming,
author = {Pablo A. Parrilo},
title = {Semidefinite Programming Relaxations for Semialgebraic Problems},
year = {2001}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible to a finite number of polynomial equalities and inequalities, it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility. The main tools employed are a semidefinite programming formulation of the sum of squares decomposition for multivariate polynomials, and some results from real algebraic geometry. The techniques provide a constructive approach for finding bounded degree solutions to the Positivstellensatz, and are illustrated with examples from diverse application fields.
Keyphrases
semialgebraic problem semidefinite programming relaxation multivariate polynomial polynomial equality semidefinite programming condition degree solution complete family main tool semidefinite programming formulation square decomposition diverse application field constructive approach real algebraic geometry finite number convex relaxation
