# 6 semester

 1 Title VARIATIONAL CALCULATION AND METHODS OF OPTIMIZATION 2 Course 3, Mechanics and mathematical modeling 3 Semester of training 6 4 Credits 3 5 Lecturer Pindrik Olga Isaakovna 6 Objectives of studying the discipline The study of the basic methods for solving classical problems of finite-dimensional optimization. Increase the level of professional competence in solving optimization problems. Further development of students’ skills in abstract mathematical thinking and the ability to apply it in specific tasks, increase their mathematical culture. As a result of the study, the student should be able to: – find the minimum and maximum points for functions defined on finite-dimensional spaces; – construct models of extremal problems in finite-dimensional spaces; – with the aid of differential convexity criteria, to check whether a given function is convex; – use optimality conditions and the Kuhn-Tucker criterion for solving convex programming problems; – use the simplex method for solving linear programming problems; – use the optimality conditions of the first and second order to solve nonlinear programming problems. 7 Requirements Mathematical analysis Algebra and Number Theory 8 Contents of the discipline Tasks of conditional and unconditional optimization. The Lagrange principle for problems with constraints of the type of equations. The Lagrange principle for problems with mixed constraints. Sufficient conditions for an extremum for problems with constraints such as equations and problems with mixed constraints. The problem of linear programming. Convex sets, separation theorems. Extreme points in canonical linear problems. Nondegenerate problems. Simplex method. The duality theory. Problems of convex programming. Optimality conditions in convex problems. The Slater condition and the Kuhn-Tucker theorem 9 References 1. Galeev EM, Tikhomirov VM A short course in the theory of extremal problems. – Moscow, Moscow State University, 1989. 2. Alekseev VM, Galeev EM, Tikhomirov VM Collection of tasks on optimization. Theory. Examples, Tasks. Study Guide: – Moscow, Science, 1984. 3. Gorokhovik V.V. Finite-dimensional optimization problems. – Minsk, 2006. 4. Bakhtin VI, Ivanishko IA, Lebedev AV, Pindrik OI Linear programming. Method. Allowance 5. Bakhtin VI, Ivanishko IA, Lebedev AV, Pindrik OI The Lagrange principle. Method. allowance 10 Teaching Methods Lectures, laboratory practice, SSI (students scientific investigation) 11 Language Russian 12 Conditions (requirements), current control test 13 Appraisal Form credit