Algorithmic convex optimization

In this talk we present the main results included in the habilitation thesis in physical and mathematical sciences. All of them are related to development of optimization schemes with improved computational abilities. This can be a computation of nearly optimal dual multipliers, or introduction of the exact termination criterion, or accelerated convergence, which goes above the upper bounds of Complexity Theory. This improvement is always achieved by a proper use of different models of the objective function. We consider the first-order methods for nonsmooth convex optimization, methods for variational inequalities, second order methods, and method for generating solutions with small relative accuracy. All schemes are supported by a comprehensive complexity analysis.