Optimization, Stability and Cylindrical Decomposition
1993 (English)Report (Other academic)
Some connections between constructive real algebraic geometry and constrained optimization are exploited. We show how the problem of determining the projection of a real-algebraic variety on a certain axis is equivalent to a problem in nonlinear programming. As an application, Grobner bases are used to deal with an optimization problem arising in the theory of local Lyapunov functions. The problems addressed are: determining critical levels of local Lyapunov functions and investigating robustness using Lyapunov functions. Since the tools used come from commutative algebra and algebraic geometry the differential equations considered are of polynomial type and the Lyapunov functions used are polynomial.
Place, publisher, year, edition, pages
Linköping: Linköping University , 1993. , 15 p.
LiTH-ISY-R, ISSN 1400-3902 ; 1472
Constrained optimization, Lyapunov theory, Stability, Polynomial differential equations, Robustness, Gröbner bases, Elimination theory, Nonlinear equation solving, Real algebraic geometry, Quantifier elimination, Commutative algebra
IdentifiersURN: urn:nbn:se:liu:diva-55591ISRN: LiTH-ISY-R-1472OAI: oai:DiVA.org:liu-55591DiVA: diva2:316323