Finding approximate solutions to minimax problems (Q1569265)

The paper is devoted to minimax problems. Solution of these problems is reduced to minimization of specially constructed functions with penalty coefficients. It is shown that the directions along which these functions decrease can be determined to a given accuracy without using penalty coefficients. The functions proposed are shown to be more suitable for finding all approximate solutions to the original problem than the functions derived in earlier studies. Application to the problem of packing identical two-dimensional spheres on a three-dimensional sphere is considered.