On the global minimum ot the objective function in a balanced circular packing problem
DOI:
https://doi.org/10.15407/dopovidi2014.06.053Keywords:
balanced circular packing, global minimum, objective functionAbstract
The paper considers the balanced packing problem of a given family of circles into a larger circle of the minimal radius as a multiextremal nonlinear programming problem. We reduce the problem to an unconstrained minimization problem of a non-smooth function by means of nonsmooth penalty functions. We propose an efficient algorithm to search for local extrema, as well as an algorithm of improvement of a lower estimate of the global minimum of the objective function. The algorithms use non-differentiable optimization methods based on Shor's r-algorithm. Computational test results are given.
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