### Methods of Optimization 1 курс (ММФ.М.2 сем.)

The purposes and problems in mastering the discipline

1. The studying of the modern methods of dynamic programming in the discrete and continuous time.

2. Application of the analytical methods obtained in the course "Mathematical Analysis", “Differential Equations”, "Partial Differential equations",  "Functional Analysis", "Theory of Probability and Mathematical Statistics" and "Stochastic modeling" to the important optimization problem such as

- optimal consumption in discrete time;

- optimal consumption and investment in discrete time;

- optimal consumption in continuous time;

- Bellman equation in discrete time;

- Hamilton-Jacobi-Bellman equation;

The role of discipline in the general structure in the Master Training Program

The course "Methods of Optimization" is an obligatory course in 10-th semester.

To study the course one needs "Differential equations", "Mathematical Analysis", "Functional Analysis", "Partial Differential equations", "Theory of Probability and Mathematical Statistics" and "Stochastic modelling".

In this course the undergraduate obtains the experiences of the application of knowledge and skills acquired in the major disciplines, readied for bachelors on mathematical specialties.

Сompetences aimed at the training of a student:

1. General:

- to be capable of self-training to study new research methods applied in different scientific and industrial problems (GC-8);

- to master the methods and techniques of Numerical Analysis by acquiring the experience in solving the basic problems on the Computer (GC-12).

2. Professional:

The course helps to form and consolidate the following professional skills (PC):

Scientific research and investigating activity:

–       To be able to get into a stated problem (PC-2);

–       To be able to formulate and analyze the result (PC-3);

–       To be able to correctly choose and use an appropriate mathematical language in a required subject area  (PC-7);

–       To understand the principal idea that the fundamental knowledge in Mathematics forms the bases for modern Computer Sciences (PC-12).

After this course the students have:

To know: the basic principles of modern dynamical programming.

To be able: to write and to study the Bellman equations and the Bellman-Hamilton-Jacoby equations.

To have: the skills to the construction of optimal solution and strategies for main optimization problems.