Abstract. An algorithm with space dilation is presented, which is the circumscribed ellipsoid method under a certain choice of tensile coefficient. It is shown that its partial case is the Yudin–Nemirovsky–Shor ellipsoid method. The application of the algorithm for solving a convex programming problem and the problem of finding a saddle point of a convex-concave function are described.

Keywords: ellipsoid method, space dilation operator, localizing ellipsoid, convex programming problem, saddle point of convex-concave function.