Linear Programming B
Code  Completion  Credits  Range  Language 

01LIPB  Z,ZK  4  2+2  Czech 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

The aim of the lecture is the exact mathematical formulation of simplex algorithm for the linear programming problem. In exact mathematical language we study primary and dual problem. As aplications, traffic problem, integer programming and example from the game theory are studied.
 Requirements:

: Basic course of Calculus and Linear Algebra (in the extent of the courses 01MA1, 01MAB24, 01LA1, 01LAB2 held at the FNSPE CTU in Prague).
 Syllabus of lectures:

1.Problem of linear programming. 2.Criterion of optimum. 3.Simplex algorithm. 4.Two simplex algorithm. 5.Example of circular in algorithm. 6.Primary and dual problems. 7.Duality theorem. 8.Farkas lemma. 9.Aplication in game theory. 10.Traffic problem. 11.Integer programming. 12.Gomory algorithm. 13.Parametric programming.
 Syllabus of tutorials:

1. Problem of linear programming, optimality conditions and unlimited conditions. 2. Simplex method. 3. Dualphase simplex method. 4. Dual simplex method. 5. An example of game theory. 6. Gomory algorithm. 7. Quadratic programming.
 Study Objective:

Knowledge: the mathematical basis for systems of linear equations and inequalities and optimaliyation. Skills: to be able to use memorized algorithms to solve specific problems of practice.
 Study materials:

Key references:[1] George B. Dantzig and Mukund N. Thapa. 1997. Linear programming 1:Introduction. SpringerVerlag. [2] M. C. Ferris, O. L. Mangasarian, and S. J. Wright. , Linear Programming with MATLAB, MPSSIAM Series on Optimization 7, SIAM, Philadelphia, PA, 2007. [3] T.C.HU, 1970, Integer Programming and Network Flows, AddisonWeslley Publishing, Menlo Park
Recommended references: [4] George B. Dantzig and Mukund N. Thapa. 2003. Linear Programming 2: Theory and Extensions. SpringerVerlag, [5] Kattta G. Murty, Linear Programming, Wiley, 1983
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 BS Aplikace softwarového inženýrství (compulsory course of the specialization)