Teacher(s)
Language
French
Prerequisites
The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Main themes
A. Analysis of real functions of several real variables (15h + 10h)
- Real functions of several real variables;
- Limits, continuity, differentiability;
- Introduction to multivariate convex optimization (free and constrained);
- Necessary conditions for optimality (Fermat's theorem) and KKT conditions.
- Introduction to the solid geometry: vector planes, hyperplanes, affine spaces, affine hyperplanes;
- Canonical and standard forms of a linear optimization problem;
- Geometry of a linear optimization problem (polytopes and vertices);
- Fundamental theorems for the existence of the solution: the alternative theorem (or Farka's lemma) and Fredholm's theorem;
- Optimality conditions;
- Simplex algorithm;
- Duality theory: primal-dual solutions; dualisation technique; duality properties; complementary slackness theorem; sensitivity analysis; marginal values;
- Examples of modeling classic business engineering and management problems as linear problems
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 | At the end of the class, the student will be able to:
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Bibliography
SYDSTER K., SYDSAETER K., HAMMOND P. (2005), Essential Mathematics for Economic Analysis, 2nd ed., Prentice-Hall.
Teaching materials
- Mathématiques de gestion 2, Syllabus.
Faculty or entity
