Semidefinite programming for optimizing convex bodies under width constraints

DOI10.1080/10556788.2010.547580zbMath1244.49054OpenAlexW2034825464WikidataQ56341009 ScholiaQ56341009MaRDI QIDQ2905348

Térence Bayen, Didier Henrion

Publication date: 27 August 2012

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556788.2010.547580

zbMATH Keywords

semidefinite programming problemconvex bodies whose support functions are trigonometric polynomialsFejér--Riesz theorem

Mathematics Subject Classification ID

Semidefinite programming (90C22) Decomposition methods (49M27) Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) (52C05)

Related Items (6)

Parametric shape optimization using the support function ⋮ Optimal design of sensors via geometric criteria ⋮ Maximization of the Steklov Eigenvalues With a Diameter Constraint ⋮ Minimization of the Eigenvalues of the Dirichlet-Laplacian with a Diameter Constraint ⋮ The log-Brunn-Minkowski inequality in ℝ³ ⋮ Numerical shape optimization among convex sets

Uses Software

• YALMIP
• PENBMI

Cites Work

• An open global volume minimization problem
• Polygonal approximation of plane convex bodies
• A direct proof of a theorem of Blaschke and Lebesgue.
• Analytic parametrization of three-dimensional bodies of constant width
• Newton's Problem of the Body of Minimal Resistance in the Class of Convex Developable Functions
• Polygons as Optimal Shapes with Convexity Constraint
• Trammel Rotors in Regular Polygons
• ON THE MAXIMIZATION OF A CLASS OF FUNCTIONALS ON CONVEX REGIONS, AND THE CHARACTERIZATION OF THE FARTHEST CONVEX SET
• Analytical Parameterization of Rotors and Proof of a Goldberg Conjecture by Optimal Control Theory
• Positive trigonometric polynomials and signal processing applications

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