Optimization Techniques

Code – 230100 Information and computer science; section: Software of computer equipment and automation systems

Qualification (degree) – Master

Description of course modules (sections, subjects):

  1. Integral linear programming problems.
  2. Extremal problems with incomplete and uncertain information.
  3. Decomposition technique for solving high dimension problems.
  4. Goal programming.
  5. Smooth convex structures in non-linear programming.
  6. Nondifferential optimization.
  7. Dynamic programming as an optimization method.
  8. Infinite-dimensional optimization of functionals. Optimization with control.

Syllabus of the course:

Branch methods. Method of sections. Additive algorithm with binary variables.

Passive and active search strategies. Methods of organizing transitions. Stochastic approximation methods. Specific character of convergence conditions. Stochastic approximation at optimal process  parameters.

Lagrangian representation and expansion in prices. Expansion in right-hand side elements. Separation of variables. Examples.

Priorities method. Weight coefficient method.

Lagrange method of multipliers. Saddle point. Kuhn-Tucker theorem.

Penalization methods. Classical Lagrangian duality. Saddle points in nonconvex programming. Generalized Lagrangians.

Recurrent forward-backward algorithms. Applications of dynamic programming.

Variational problem. Pontryagin's maximum principle for optimal control. Relation between these problems. Numerical computation.

Teaching methods:

  • lectures,
  • classroom group training directed by a teacher,
  • students’ independent work performed according to the teacher’s task in classrooms and on an extracurricular basis, including use of technical training aids (compulsory),
  • tutorials.

Total hours – 108.

Total credits – 3.

Laboratory work – not applicable.

Form of interim assessment – pass/fail exam.

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