Lecturer(s)


Ženčák Pavel, RNDr. Ph.D.

Course content

1. Historical overview of linear programming, general formulation of linear programming problems. 2. Graphic solution of simple problems. Application of linear programming. 3. Selected pieces of knowledge of convex analysis. 4. Basic theoretical concepts of linear programming and geometrical view to solution. 5. Fundamentals of nonlinear optimization and convex programming. 6. The duality theory in linear programming and its economic interpretation. 7. Algorithm of simplex method in standard form and spreadsheet computation. 8. Derivation of the simplex method using linear algebra and geometry, treatment for degenerate problems, computational complexity of the simplex method. 9. Derivation of the simplex method using convex programming, the revised simplex method and its comparison with the standard simplex method. 10. Dual simplex method and its application. 11. The transportation problem: Formulation of the problem, special methods for computing the initial and optimal solutions. 12. Interior points methods. Integer linear programming: Introduction to principles of basic methods (branch and bound method, cutting plane methods).

Learning activities and teaching methods

Lecture, Demonstration, Projection (static, dynamic)
 Attendace
 52 hours per semester
 Preparation for the Course Credit
 40 hours per semester
 Homework for Teaching
 20 hours per semester
 Semestral Work
 10 hours per semester

Learning outcomes

The course introduces the theory and methods for solutin of linear programming problems.
Comprehension Understand the basic terms in optimization and the methods for solution of linear programming problems.

Prerequisites

Basic knowledge of mathematical analysis and linear algebra.

Assessment methods and criteria

Written exam, Seminar Work
Credit: the student has to pass written tests, understand the subject and program a given algorithm.

Recommended literature


G.B. Dantzig. (1963). Linear programming and extensions. North Holland.

G.B. Dantzig. (1966). Lineárne programovanie a jeho rozvoj. SVTL Bratislava.

J. Nocedal, S. Wright. (1999). Numerical Optimization. Springer.

J.Plesník, J Dupačová, M. Vlach. (1990). Lineárne programovanie. ALFA, Bratislava.

J.Švrček. (1995). Lineární programování v úlohách. Vydavatelství UP Olomouc.

Ženčák, P. (2013). Lineární programování. Olomouc: Univerzita Palackého v Olomouci.
