Minimum ellipsoid bounds for solutions of polynomial systems via sum of squares

DOI10.1007/s10898-005-2099-2zbMath1097.90039arXivmath/0411122OpenAlexW2090225690MaRDI QIDQ816068

James W. Demmel, Jia-Wang Nie

Publication date: 20 February 2006

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411122

zbMATH Keywords

EllipsoidSemidefinite programming (SDP)PerturbationPolynomial systemReal algebraic geometrySum of squares (SOS)

Mathematics Subject Classification ID

Semidefinite programming (90C22)

Related Items

Representations of positive polynomials on noncompact semialgebraic sets via KKT ideals, Enclosing ellipsoids and elliptic cylinders of semialgebraic sets and their application to error bounds in polynomial optimization, Global optimality conditions and optimization methods for polynomial programming problems, Global optimization of general nonconvex problems with intermediate polynomial substructures

Uses Software

• Sostools

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the complexity of Schmüdgen's Positivstellensatz
• The \(K\)-moment problem for compact semi-algebraic sets
• Semidefinite programming relaxations for semialgebraic problems
• Ellipsoidal bounds for uncertain linear equations and dynamical systems
• Complexity estimates for the Schmüdgen Positivstellensatz
• Global Optimization with Polynomials and the Problem of Moments
• SOSTOOLS and Its Control Applications
• A representation theorem for certain partially ordered commutative rings