New computer methods for global optimization
New computer methods for global optimization
Journal of Combinatorial Theory Series A
The largest small n-dimensional polytope with n + 3 vertices
Journal of Combinatorial Theory Series A
The minimum diameter octagon with unit-length sides: Vincze's wife's octagon is suboptimal
Journal of Combinatorial Theory Series A
A correction to "The largest small n-dimensional polytope with n + 3 vertices"
Journal of Combinatorial Theory Series A
The small octagon with longest perimeter
Journal of Combinatorial Theory Series A
Recognition of largest empty orthoconvex polygon in a point set
Information Processing Letters
Piece adding technique for convex maximization problems
Journal of Global Optimization
The small hexagon and heptagon with maximum sum of distances between vertices
Journal of Global Optimization
Enumerating isodiametric and isoperimetric polygons
Journal of Combinatorial Theory Series A
A linear-time combinatorial algorithm to find the orthogonal hull of an object on the digital plane
Information Sciences: an International Journal
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Consider a convex polygon V n with n sides, perimeter P n , diameter D n , area A n , sum of distances between vertices S n and width W n . Minimizing or maximizing any of these quantities while fixing another defines 10 pairs of extremal polygon problems (one of which usually has a trivial solution or no solution at all). We survey research on these problems, which uses geometrical reasoning increasingly complemented by global optimization methods. Numerous open problems are mentioned, as well as series of test problems for global optimization and non-linear programming codes.