Recent Advances in Structural Optimization

In this paper we present the main directions of research in Structural Convex Optimization. In this field, we use additional information on the structure of specific problem instances for accelerating standard Black-Box methods. We show that the proper use of problem structure can provably accelerate these methods by the order of magnitudes. As examples, we consider polynomialtime interior-point methods, smoothing technique, minimization of composite functions and some other approaches. Mathematics Subject Classification (2010). Primary 90C25; Secondary 90C06.