Radii minimal projections of polytopes and constrained optimization of symmetric polynomials

DOI10.1515/ADVGEOM.2006.005zbMath1108.52010arXivmath/0311017OpenAlexW2962732036MaRDI QIDQ5488627

René Brandenberg, Thorsten Theobald

Publication date: 22 September 2006

Published in: advg (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0311017

zbMATH Keywords

projectionpolytopesymmetric polynomialsregular simplexpolynomial optimizationouter radiusenclosing cylinder

Mathematics Subject Classification ID

Semidefinite programming (90C22) (n)-dimensional polytopes (52B11) Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Fitting enclosing cylinders to data in \(\mathbb R^n\), Successive radii and Minkowski addition, Holding a regular pyramid by a circle, Intrinsic volumes and successive radii, On the families of successive radii and the sum of convex sets, Classification of the congruent embeddings of a tetrahedron into a triangular prism, Regular simplices passing through holes, About the algebraic solutions of smallest enclosing cylinders problems

Uses Software

• GloptiPoly

Cites Work

• Inner and outer \(j\)-radii of convex bodies in finite-dimensional normed spaces
• Semidefinite programming relaxations for semialgebraic problems
• High-dimensional shape fitting in linear time
• Radii of regular polytopes
• Algebraic methods for computing smallest enclosing and circumscribing cylinders of simplices
• Smallest enclosing cylinders
• Computational complexity of inner and outer \(j\)-radii of polytopes in finite-dimensional normed spaces
• A Nullstellensatz and a Positivstellensatz in semialgebraic geometry
• Global Optimization with Polynomials and the Problem of Moments
• Deterministic and randomized polynomial‐time approximation of radii
• APPROXIMATING THE DIAMETER, WIDTH, SMALLEST ENCLOSING CYLINDER, AND MINIMUM-WIDTH ANNULUS
• Optimization of Polynomials on Compact Semialgebraic Sets
• GloptiPoly