Alternative course on additional optimization chapters

The main aim is to deepen students' knowledge in the field of optimization methods in large-dimensional spaces. Special emphasis will be placed on modern numerical methods for variational inequalities and saddle problems. Different classes of saddle problems are popular, in particular, due to the applications to training of so-called generative-state networks (GAN). It is also planned to present theoretical results on the convergence of first-order methods for some types of non-smooth optimization problems for convex, quasi-convex and weakly convex functions with different smoothness assumptions. As applications, we can consider binary classification problems by the support vector machine (SVM), mechanical design (Truss Topology Design), weakly convex nonlinear regression problems, phase retrieval, matrix recovery, etc