MAU34801 The theory of linear programming
| Module Code | MAU34801 |
|---|---|
| Module Title | The theory of linear programming |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Sergey Mozgovoy |
| Module Prerequisites | MAU11100 Linear algebra |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 20% towards the overall mark.
- The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.Capping of reassessments applies to Theoretical Physics (TR035) students enrolled in this module. See full text at https://www.tcd.ie/teaching-learning/academic-affairs/ug-prog-award-regs/derogations/by-school.php Select the year and scroll to the School of Physics.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Determine optimal solutions of simple linear programming problems using the simplex method.
- Justify with reasoned logical argument the basic relationships between feasible and optimal solutions of a primal linear programming problem and those of the corresponding dual programme.
- Explain why the simplex method provides effective algorithms for solving linear programming problems.
- Explain applications of linear algebra and linear programming in contexts relevant to mathematical economics.
Module Content
- Introduction to linear programming problems.
- The Transportation Problem.
- Methods for solving linear programming problems based on the simplex algorithm of George Danzig.
- Duality in the theory of linear programming problems.
- Farkas's Lemma.
- Applications of Farkas's Lemma to prove duality theorems in the theory of linear programming problems.
- The Karush-Kuhn-Tucker conditions characterizing optimal solutions of nonlinear programming problems.