Schedule
... see timetable section [DM554-H1]
[DM545-H1]
[DM545-H2]
[DM545-O1]
You can import the schedule in your calendar using the iCalendar file at
this DM554-H1, DM545-H1, DM545-H2, DM545-O1.
Introductory Classes
Linear Algebra Part
| Date | Topic and Slides | Literature and Assignments |
|---|
| 1 | 02.02 | Introduction. Preliminaries | [AH p 1-8] |
| 2 | 04.02 | Matrices and Vectors | [Le s 1.3-1.4] |
| 3 | 11.02 | Geometric Insight | |
| 4 | 17.02 | Systems of Linear Equations | [Le s 1.1-1.2, 1.5] |
| 5 | 04.03 | LU-factorization (see below), Determinants, Matrix Inverse | [Le s 1.5, 2.1-2.3] |
| 6 | 08.03 | Rank, Range and Vector Spaces | [Le s 3.1,3.2,3.6] |
| 7 | 11.03 | Vector Spaces, Linear Independency, Bases, Dimensions | [Le s 3.3,3.4,3.6] Assignment 0 (sol) Reexam |
| 8 | 16.03 | Linear Transformations | [Le 4.1,4.2,3.5] |
| 9 | 18.03 | Diagonalisation | [Le s 4.3, s 6.1,6.3] |
Linear and Integer Programming Part
| Date | Topic and Slides | Literature | Assignments |
|---|
| 1 | w13 | Introduction - Linear Programming, Notation | [ Notes ] | |
| | Resource allocation in factory planning. Diet problem. | [L1,L2] [HL ch 1,2,3] | |
| | Linear programming problems and geometrical interpretation. | [MG ch 1,2, Appendix] [L3] | |
| | History. Fourier & Moutzkin elimination | [Da] [ wiki ] | |
| 2 | w13 | Linear Programming, towards the Simplex Method | [ Notes ] | |
| | Notation: polyhedral analysis | [MG ch 4] [HL sc 5.1] [L5] | |
| | Linear programming theory, Fundamental theorem | [L4,L6] | |
| | Gaussian Elimination | [ wiki ] [L4] | |
| 3 | apr10 | Simplex Method | [ Notes ] | |
| | Simplex method, tableaux and dictionaries | [MG ch 5] [HL sc 4.1-4.4] | |
| 4 | apr13 | Exception Handling and Initialization | [ Notes ] | |
| | Exception handling and degeneracies in simplex method. Pivot rules | [MG ch 5], [HL sc 4.5] | |
| 5 | apr17 | Duality | [ Notes ] | |
| | Duality: bounding and multipliers approach | [HL sc 6.1-6.4] | |
| | Weak/strong duality theorems and complementary slackness theorem | [MG sc 6.1-6.3] | |
| 6 | apr20 | More on Duality | [ Notes ] | |
| | Geometric Interpretation, Duality by Lagrangian relaxation | [Ch ch 10] [CL ch 2] | |
| | Dual Simplex, Sensitivity Analysis | [Va sc 7.1] [HL sc 7.1, 4.7] | |
| 7 | apr24 | Revised Simplex Method | [ Notes ] | Assignment 1 |
| | | [HL ch 5] [Va 6.1-6.5] | (FPMM) (sol) |
| | | [ Ch ch 7 ] | (PS) (sol) Rev |
| 8 | apr27 | Polyhedra and Farkas Lemma | [SR, W5-5 W5-7] [MG sc 6.4] | |
| 9 | apr28 | Integer Programming - Modeling Examples | [MG ch 3] [Wo ch 1] | |
| 10 | may04 | Integer Programming - More on Modeling, Formulations | [Wi ch 9.1-9.5] [Wo ch 2] | |
| 11 | may11 | Relaxations, Well Solved Problems | [Wo sec. 3.2-3.5 (BB)] [CL ch 7] | |
| | Convex hull description, Total unimodular matrices | | |
| 12 | may15 | Network Flows | [CL ch 4,6,7] | Assignment 2 |
| | Min cost flow, Maximum flow, Shortest path, multicommodity flow | | (KP-TSP) (sol) |
| | Duality in network flows | | (SPAP) (sol) |
| 13 | may17 | Cutting Planes - Branch and Bound | [ Notes ] | |
| | Valid Inequalities. Chvatal Gomory cuts. | [Wo ch 7, 8.1-8.6 (BB)] | |
| | Cutting plane algorithm. Gomory's fractional cutting plane algorithm | | |
| | Branch and Bound, examples | | |
| 14 | may29 | More on Branch and Bound, Modelling and Preprocessing | | |
| | Branching strategies, Assignment and Transportation Problems | [Wo ch 7] [AOM sec 1.2 (BB)] [KN] | |
| | Preprocessing, Modelling Piecewise linear functions | [Wi, ch 9 (BB)] | |
Exercises
Linear and Integer Programming Part
Literature
Linear and Integer Programming Part:
- [AMO] R.K. Ahuja, T.L. Magnanti and J. Orlin. Network Flows: Theory,
Algorithms, and Applications. Prentice Hall, 1993
- Other References
- [Ch] V. Chvatal. Linear Programming. W.H.Freeman, 1983
Assessment
- Three/Two obligatory assignments with pass/fail assessment by the
teacher. The assignments are practice oriented and must be passed to
attend the written exam.
- Written exam on June 22, 4 hours, Danish 7 grade scale, external
examiner (Dr. Mette Gamst)
- Hints: being acquainted with some of these tools (or their equivalent
in your system) would help you to digitalize your solutions more easily and faster:
Course Evaluation by Students
Date: 2015-08-19T08:26+0200
Author: marco
Org version 7.9.3f with Emacs version 24
Validate XHTML 1.0
|