Convex analysis. Osipenko K.Yu.

The book is devoted to the basics of convex analysis and its application to the tasks of linear programming. It is based on lecture courses, read by the author at the Mechanical and Mathematics Faculty of Moscow State University named after MV Lomonosov and at the faculty of applied mathematics and management of the MIPT.

The presentation of the basics of convex analysis is carried out in a simple, affordable language, does not require additional knowledge, except for the very initial concepts on the theory of linear normalized spaces. Much attention is paid to convex extreme tasks and the concept of duality. The symptom-method of solving linear programming problems and the potential method for solving a transport problem is described in detail. Examples of solutions to these problems are given.

The book can be used by students and graduate students studying in mathematical specialties, teachers and scientists.