On the global minimum in a balanced circular packing problem

Abstract

The paper considers 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 unconstrained minimization problem of a nonsmooth function by means of nonsmooth penalty functions. We propose an efficient algorithm to search for local extrema and an algorithm for improvement of the lower bound of the global minimum value of the objective function. The algorithms employ nonsmooth optimization methods based on Shor’s r-algorithm. Computational results are given.