The paper analyses a class of nonlinear optimization problems with special restrictions. We propose a concept for solving the auxiliary problem, for which we calculate complexity. We also assess the maximum number of elementary operations and describe the optimal algorithm for performing numerical calculations with complexity O(nm2, N). In practical situations, if m << n, then the value of m2 is much smaller than the value of n, thus it can be considered as a constant, resulting in the complexity O(n2). In other words it's almost the same as for the approximation methods.