This course introduces students to the basic optimization methods and their practical applications to problems posed within mechanical systems.

Students learn basic tools of variational calculus and optimal control for dynamical systems and to use these tools in solving a variety of problems in structural and process design within mechanics and engineering in order to optimize the values of selected physical parameters.

This course covers the following topics. Elements of variational calculus. Hamilton's principle. variational problems with constraints. Variational calculus in terms of canonical variables with applications in mechanics. Canonical transformations and the Hamilton-Jacobi equation. Direct variational methods with applications in heat transfer problems. Optimal control problem by means of variational calculus. Constrained optimal problems. The maximum principle of Pontryagin. Applications in motion control and structural design. The Belman dynamical programming theory in discrete and continuous multistage processes. Elements of nonsmooth/nonconvex optimization. Examples.

Lectures, auditory exercises, demonstration of computer tools. Homeworks, as a check of understanding and usage of the introduced notions that can be done within groups. Either a practical examination part -- two problems done by them own -- or seminar work based on a real problem presented in periodicals. Individual work with each of the groups which extends the knowledge and skills in analysis and formulation of an optimization problem as well its numerical solving. The examination ends with a final talk on the introduced notions and skills in solving optimization problems.