Abstract
AbstractThe 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.
Highlights
The Charged Balls Method is based on physical ideas
We can assume that ∇f (x) ≠ 0 for all x ∈ bd X, where bd X is the boundary of the set X
Both of these effects are associated with the inertia which is brought by the presence of mass
Summary
– If it is fulfilled, we take xk as the solution and exit the algorithm. – If it is not, increment k by one and return to the first step. Where f : Rn → R is a convex twice continuously differentiable function and 0 ∉ X. We can assume that ∇f (x) ≠ 0 for all x ∈ bd X, where bd X is the boundary of the set X
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