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Mihály Markót

Rigorous packing of unit squares into a circle

Published: 2018/04/03
  • Mihály Markót
  • Arnold Neumaier
  • Tiago Montanher
  • Categories Global Optimization

    Let $r_{n}$ be the radius of the smallest circle into which one can pack $n$ non-overlapping unit squares that are free to rotate. For $n = 1, 2$, $r_{1} = \frac{\sqrt{2}}{2}$ and $r_{2} = \frac{\sqrt{5}}{2}$ are proved to be optimal. For $n \geq 3$ only guesses of $r_{n}$ are known. This paper introduces a computer-assisted … Read more

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    Keywords

    alternating direction method of multipliers approximation algorithms augmented lagrangian method bilevel optimization Branch-and-Bound branch-and-cut chance constraints column generation combinatorial optimization complexity compressed sensing conic optimization convex optimization cutting planes decomposition derivative-free optimization distributionally robust optimization duality dynamic programming first-order methods global convergence global optimization heuristics integer programming interior point methods large-scale optimization linear programming machine learning mixed-integer linear programming mixed-integer nonlinear programming mixed-integer programming nonconvex optimization nonlinear optimization nonlinear programming nonsmooth optimization optimal control optimization proximal point algorithm quadratic programming robust optimization semidefinite programming stochastic optimization stochastic programming trust-region methods unconstrained optimization

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