The small octagon with longest perimeter

DOI10.1016/j.jcta.2006.04.002zbMath1259.90096OpenAlexW2042105004MaRDI QIDQ857420

Frédéric Messine, Pierre Hansen, Charles Audet

Publication date: 14 December 2006

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2006.04.002

zbMATH Keywords

diameterinterval arithmeticperimeteroctagon

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26)

Related Items

Extremal problems for spherical convex polygons, Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO, Numerical certification of Pareto optimality for biobjective nonlinear problems, Maximal perimeter, diameter and area of equilateral unit-width convex polygons, Searching approximate global optimal Heilbronn configurations of nine points in the unit square via GPGPU computing, Tight bounds on the maximal perimeter of convex equilateral small polygons, GLOMIQO: global mixed-integer quadratic optimizer, Maximal Area of Equilateral Small Polygons, Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2, Small polygons with large area, The small hexagon and heptagon with maximum sum of distances between vertices, The small octagons of maximal width, Extremal problems for convex polygons, Enumerating isodiametric and isoperimetric polygons, QPLIB: a library of quadratic programming instances, Isoperimetric polygons of maximum width, Tight bounds on the maximal perimeter and the maximal width of convex small polygons

Uses Software

• INTOPT_90

Cites Work

• A discrete isoperimetric problem
• The largest small hexagon
• Rigorous global search: continuous problems
• The largest small octagon
• The minimum diameter octagon with unit-length sides: Vincze's wife's octagon is suboptimal
• A branch and cut algorithm for nonconvex quadratically constrained quadratic programming
• On convex polygons of maximal width
• A Deterministic Global Optimization Algorithm for Design Problems
• Deterministic global optimization using interval constraint propagation techniques
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