# 6 semester

 1 Name of the discipline EXTREME OBJECTIVES AND VARIATIONAL CALCULUS 2 Study course, specialty 3, Mathematics (scientific and pedagogical activity) 3 Semester of study 6 4 Amount of credits 3 5 Lecturer’s S.N.P. Romashchenko Galina Stanislavovna 6 Aims of the study The study of the basic methods for solving classical problems. Increase the level of professional competence in solving optimization problems. Further development of students’ skills in abstract mathematical thinking and skills applies it to a specific task, increasing 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; – to build models of extremal problems in finite-dimensional spaces; – with the aid of differential convexity criteria, to check whether a given function is convex; – the use of optimality conditions and the Kuhn-Tucker criterion for solving convex programming problems; – use the simplex method for solving linear programming problems; – the use of optimality conditions of the first and second order for solving nonlinear programming problems. 7 Prerequisites 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 Recommended literature 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 Methods of teaching Lectures, laboratory practice, SSI (students scientific investigation) 11 Language of teaching Russian 12 Knowledge control and requirements Tests 13 Certification form credit