Course details

Optimization 2

SO2 Acad. year 2014/2015 Summer semester 4 credits

Current academic year

The course focuses on advanced optimization models and methods of solving engineering problems. It includes especially stochastic programming (deterministic reformulations, theoretical properties, and selected algorithms) and selected areas of integer and dynamic programming.

Guarantor

Popela Pavel, RNDr., Ph.D. (IM DSO)

Language of instruction

Czech

Completion

Examination

Time span

Department

Faculty of Mechanical Engineering (FSI)

Subject specific learning outcomes and competences

The course focuses on advanced optimization models and methods of solving engineering problems. It includes especially stochastic programming (deterministic reformulations, theoretical properties, and selected algorithms) and selected areas of integer and dynamic programming.

Learning objectives

The course objective is to develop the advanced knowledge of sophisticated optimization techniques as well as the understanding and applicability of principal concepts.

Prerequisite knowledge and skills

The presented topics require basic knowledge of optimization concepts (see FSI-SOP). Standard knowledge of probabilistic and statistical concepts is assumed.

Study literature

  • Kall, P. - Wallace, S.W.: Stochastic Programming, Wiley 1994.
    Klapka, J. a kol: Metody operačního výzkumu, VUT, 2000.
    Birge, J.R. - Louveaux, F.: Introduction to Stochastic Programing, Springer, 1997.
    Prekopa, A: Stochastic Programming, Kluwer, 1996.

Syllabus of seminars

Syllabus of lectures:
  1. Underlying mathematical program.
  2. WS and HN approach.
  3. IS and EV reformulations.
  4. EO, EEV, EVPI and VSS.
  5. MM and VO, the solution of the large problems.
  6. PO and QO, relation to integer programming.
  7. Deterministic and probabilistic constraints, the use of recourse.
  8. WS theory - convexity and measurability.
  9. WS theory - probability distribution identification.
  10. Twostage problems, classification and modelling.
  11. Basic results in convexity of SPs.
  12. Applied twostage programming.
  13. Dynamic programming and multistage models

Syllabus of computer exercises:
  1. Underlying mathematical program.
  2. WS and HN approach.
  3. IS and EV reformulations.
  4. EO, EEV, EVPI and VSS.
  5. MM and VO, the solution of the large problems.
  6. PO and QO, relation to integer programming.
  7. Deterministic and probabilistic constraints, the use of recourse.
  8. WS theory - convexity and measurability.
  9. WS theory - probability distribution identification.
  10. Twostage problems, classification and modelling.
  11. Basic results in convexity of SPs.
  12. Applied two-stage programming.
  13. Dynamic programming and multistage models.

Progress assessment

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Controlled instruction

The attendance at seminars is required as well as active participation. Passive or missing students are required to work out additional assignments.

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