Tag · 3 problems · 1 field

Open problems tagged optimization

3 problems in the Math Lab index touch optimization. Each carries a precise statement, an honest status, and a computational line of attack.

Hadamard's maximal determinant problemGeometry & Packinguntouched

What is the largest possible determinant of an n×n matrix with entries ±1? Hadamard's bound n^(n/2) is attained only at Hadamard orders; other orders are subtler.

Square packing in a squareGeometry & Packinguntouched

Find the smallest square that contains n unit squares without overlap. Tilted packings beat axis-aligned ones surprisingly early.

Tammes problemGeometry & Packinguntouched

Place n points on a sphere maximizing the minimum pairwise distance. Find and certify the optimal configurations.