  This textbook is based on lectures given by the authors at MIPT (Moscow), HSE
(Moscow), FEFU (Vladivostok), V.I. Vernadsky KFU (Simferopol), ASU (Republic of
Adygea), and the University of Grenoble-Alpes (Grenoble, France). First of all,
the authors focused on the program of a two-semester course of lectures on
convex optimization, which is given to students of MIPT. The first chapter of
this book contains the materials of the first semester ("Fundamentals of convex
analysis and optimization"), the second and third chapters contain the
materials of the second semester ("Numerical methods of convex optimization").
  The textbook has a number of features. First, in contrast to the classic
manuals, this book does not provide proofs of all the theorems mentioned. This
allowed, on one side, to describe more themes, but on the other side, made the
presentation less self-sufficient. The second important point is that part of
the material is advanced and is published in the Russian educational
literature, apparently for the first time. Third, the accents that are given do
not always coincide with the generally accepted accents in the textbooks that
are now popular. First of all, we talk about a sufficiently advanced
presentation of conic optimization, including robust optimization, as a vivid
demonstration of the capabilities of modern convex analysis.
