Global Optimization in Geometry — Circle Packing into the Square

Optimization in Surgical Operation Design

“…This would be in accordance with what we have learned in the determination of optimal circle packing [4,5]. Also other, less dimension sensitive global optimization methods can help, such as the Multilevel Coordinate Search [2].…”

“…In this way the optimal surgery operation design problem belongs to discrete geometrical optimization [5].…”

Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming

“…. , n. This geometric problem has been extensively studied in the global optimization literature [6,13]. Via a well-known transformation the problem is equivalent to the "point packing" problem…”

Global optimization algorithms for bound constrained problems

“…The use of the known optimum value within an optimization algorithm is not typical, still it is realistic in several cases, as explained in Hirsch et al [55], but also according to the experiments e.g. with circle packing problems (see Markót and Csendes [67], and Szabó et al [110]). For each problem, 100 independent runs of GLOBAL were completed.…”

“…Just to name some of the numerous applications of global optimization using interval arithmetic, we point on some recent publications: these techniques were used to solve hard mathematical problems arising in the eld of qualitative analysis of dynamical systems (see Csendes et al [31,30], and Bánhelyi et al [6]) and discrete geometry, for optimal packing of circles in the square (see Markót and Csendes [67], and Szabó et al [110]). Global optimization methods have also been applied for theoretical chemical problems in Balogh et al [4], and for the evaluation of bounding methods in Tóth et al [111].…”