Easter 2017

** LECTURE NOTES**

- lecture 1 An example; notation and definitions; Lagrangian suffiency
- lecture 2 Lagrangian method; inequality constraints and complementary slackness
- lecture 3 Lagrangian necessity; shadow prices; convex sets and functions
- lecture 4 Definition of the dual problem; dual problem of a linear program; fundamental theorem of linear programming
- lecture 5 Extreme points; basic feasible solutions of linear programs
- lecture 6 Simplex algorithm in theory; non-degeneracy
- lecture 7 Simplex algorithm in practice; an example
- lecture 8 Perturbations of linear programs; the two-phase method
- lecture 9 Zero-sum games; pure and mixed strategies; saddle points; criterion for optimality; dominating strategies; methods of solution
- lecture 10 The maximum flow problem; Ford-Fulkerson algorithm; max-flow min-cut theorem
- lecture 11 Proof of the max-flow min-cut theorem; an example application
- lecture 12 The transportation problem; the transportation algorithm

** EXAMPLE SHEETS**

- example sheet 1 of 2
- example sheet 2 of 2

**OTHER RESOURCES**

- A note filling in some of the details of the fundamental theorem of linear programming.
- A Ford-Fulkerson algorithm slideshow.
- A transportation algorithm slideshow.
- Free online book on Convex Optimization, by Boyd and Vandenberghe
- Dr. Fischer's page
- Dr. Kennedy's page
- Prof. Weber's page