Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT
| MMA0006 | Linear Optimization |
| Teaching Staff in Charge |
Assoc.Prof. BRECKNER Brigitte Erika, Ph.D., brigitte math.ubbcluj.ro |
| Aims |
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An introduction in linear optimization in R^n is offered, including its theoretical foundations (properties of polyhedra and consequences of these properties in the case of linear optimization problems), numerical algorithms for solving linear optimization problems, elements of matrix game theory |
| Content |
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1. Introduction in linear optimization; mathematical models; the general optimization problem in R^n; the special case of linear optimization problem in R^n.
2. Elements of convex analysis in the n-dimensional euclidean space (convex sets; cones; polyhedra; extremal points of convex sets; extremal points and polyhedra faces) 3. Alternative theorems for linear systems of equations and inequations in R^n 4. The study of linear optimization problems in R^n (solutions set properties; characterization of solutions; linear optimization problems in canonical form and linear optimization problems in standard form) 5. Numerical methods for solving linear optimization problems (graphical method for linear optimization problems in R^2; simplex algorithm for linear optimization problems in canonical and standard form; the two phases method for linear optimization problems in standard form) 6. The duality of linear optimization problems (economy interpretations; duality theorems) 7. Applications of linear optimization to the study of matrix games |
| References |
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1) BRECKNER, B.E., De la poliedre la jocuri matriceale. O introducere in optimizarea liniara, EFES, Cluj-Napoca, 2007.
2) BRECKNER, B.E., POPOVICI, N., Convexity and Optimization. An Introduction, EFES, Cluj- Napoca, 2006. 3) BRECKNER, B.E., POPOVICI, N., Probleme de cercetare operationala, EFES, Cluj-Napoca, 2006. 4) Breckner W.W., Cercetare operationala, Cluj-Napoca: Universitatea $Babes-Bolyai$, Facultatea de matematica, 1981. 5) Breckner W.W., Duca I. D., Culegere de probleme de cercetare operationala, Cluj-Napoca: Universitatea $Babes-Bolyai$, Facultatea de Matematica si Informatica, 1983. 6) VANDERBEI, R. J., Linear Programming. Foundations and extensions, International Series in Operations Research&Management Science 37, Kluwer Academic Publishers, Boston, 2001. 7) Webster, R., Convexity, Oxford University Press, New York, 1994. |
| Assessment |
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Written and oral examination (the last one is not compulsory). The written exam evaluates the ability to apply the theory in problems solving (both of computational nature, by applying one of the algorithms explained in the course, and theoretical). At the end of the semestre, each student has to write project about a certain real linear optimization problem occuring in economy. This problem has to be determined by documentation in a company.
The evaluation of this project is 20% of the final grade, the exam is 80%. |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |