Algorithms for approximate calculation of the minimum of a convex function from its values

The paper deals with a numerical minimization problem for a convex function defined on a convex $n$-dimensional domain and continuous (but not necessarily smooth). The values of the function can be calculated at any given point. It is required to find the minimum with desired accuracy. A new algorithm for solving this problem is presented, whose computational complexity as $n\to\infty$ is considerably less than that of similar algorithms known to the author. In fact, the complexity is improved from $Cn^7\ln^2(n+1)$ [4] to $Cn^2\ln(n+1)$.