Modifications of the Charged Balls Method

Majid Abbasov 1  and Faramoz Aliev 2
  • 1 St. Petersburg State University, SPbSU, , 199034, St. Petersburg
  • 2 St. Petersburg State University, SPbSU, , 199034, St. Petersburg


The Charged Balls Method is based on physical ideas. It allows one to solve problem of finding the minimum distance from a point to a convex closed set with a smooth boundary, finding the minimum distance between two such sets and other problems of computational geometry. This paper proposes several new quick modifications of the method. These modifications are compared with the original Charged Ball Method as well as other optimization methods on a large number of randomly generated model problems.

We consider the problem of orthogonal projection of the origin onto an ellipsoid. The main aim is to illustrate the results of numerical experiments of Charged Balls Method and its modifications in comparison with other classical and special methods for the studied problem.

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  • [1] Abbasov M. E., Charged ball method for solving some computational geometry problems, Vestnik St. Petersburg University, Mathematics, 2017, 50(3), 209–216

  • [2] Minu M., Mathematical Programming. Theory and Algorithms [in Russian], Nauka, Moscow, 1990

  • [3] Nocedal J., Wright S., Numerical Optimization, Springer-Verlag New York, 2006

  • [4] Kochenderfer Mykel J., Wheeler Tim A., Algorithms for Optimization, The MIT Press, Massachusetts, 2019

  • [5] Lin A., Han S. P., On the distance between two ellipsoids, SIAM J. Optim., 2002, 13, 298–308

  • [6] Bland R. G., Goldfarb D., Todd M. J., The ellipsoid method: A survey, Operations Research, 1981, 29(6), 1039–1091


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