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A new generation of engineers
A new generation of engineers

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Numerical methods for mathematical optimization - 4FME1006

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  • Number of hours

    • Lectures : 9.0
    • Tutorials : 3.0
    • Laboratory works : 0
    • Projects : 0
    • Internship : 0
    • Written tests : 0
    ECTS : 12.0
  • Officials : Gerard MORTHA

Goals

Learning outcomes :

  • To shape a linear or non-linear programming problem,
  • To understand and use the simplex algorithm,
  • To understand and use the classic algorithms of non-linear programming,
  • To shape and solve optimization problems in Excel using the solver.
Contact Gerard MORTHA

Content

1. Recalls
-Recalls on matrix calculation (simple matrix operations)
-Scalar multivariables functions and vectorial functions
-Gradient, Hessian, curvature of a space function.
-Linear and quadratic functions
-Taylor development of a multivariable function
2. Resolution of non-linear algebraic systems of equations
-Iterative method
-Newton Raphson method

3. Non-linear optimization
-Heuristic methods
-Methods using the gradient only
-Methods using the gradient and the Hessian (Newton type).
-Unidimensional optimization

4. Linear optimization
-Simplexe algorithm
-Application to production management

Laboratory work session (TD session) :
The discovery and use of the EXCEL Solver for the resolution of selected problems and case studies.

Targeted competence -> Develop innovative solutions



Prerequisites

Engineering Bachelor level - 1st year cursus in Mathematics

Tests

Semester 8 - The exam is given in english only 

Written (individual) examination during the TD session.



note = note du TD

Calendar

The course exists in the following branches:

Additional Information

Semester 8 - This course is given in english only EN

Curriculum->Pagora Engineer - Student->Semester 8
Curriculum->Master Bio2->Semester 8


Sécurité-Environnement

Bibliography

MINOUX Michel Programmation mathématique, théorie et algorithmes. 2e éd. Paris : TEC/DOC Lavoisier, 2007.
MINOUX Michel Programmation mathématique, théorie et algorithmes. 2e éd. Paris : Dunod (2 vol.) 1987 - 1989 (294 p. - 276 p.).
FLETCHER Roger Practical methods of optimization. Chichester [etc.] : John Wiley & Sons, 1987

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Date of update July 24, 2020

Université Grenoble Alpes