Mixed method for solving the general convex programming problem

Conclusion Let us return to the claim that we made at the beginning: given the existing level of computers, computational mathematics must not ignore new opportunities for finding results that have been impossible until very recently. In our view, the proposed mixed method is consistent with technological progress: all known problems have been solved in acceptable time, and not in a single case has the method failed to produce a solution. Although we can always dispute claims of the kind made above, our calculations nevertheless convince that the algorithms proposed in this article may be used to solve a fairly broad class of problems, and in particular semidefinite programming problems [7, 17]. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 121–134, July–August, 1998.