Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master

SUBJECT

Code
Subject
MMA1008 Numerical Methods in Optimization
Section
Semester
Hours: C+S+L
Category
Type
Mathematics
4
2+1+0
speciality
optional
Teaching Staff in Charge
Prof. LUPSA Liana, Ph.D.,  llupsamath.ubbcluj.ro
Aims
Getting to know some significant numerical methods for solving the optimization problems.
Content
Numerical methods to minimize the unimodal functions.
2. Numerical methods to minimize the unconstrained function: decreasing methods, conjugated directions methods, relaxation methods, methods whithout the hypothesis of differentiability.
3. Numerical methods with feasible directions,
4 .Numerical methods based on reducing constrained problems to unconstrained ones
5. Cutting methods,
6. Inner point methods
7. Branch and bound methods.
8. Specific methods to solve fractional, hyperbolic and quadratic programming problems are studied, too.
9. Methods to solve liniar optimisation problems: simplex methods, Hacian@s method, Karmarkar@s method.
References
1. ANDREI N.: Programare matematica avansata. Teorie, metode computationale, aplicatii. Bucuresti: Ed. Tehnica, 1999.
2. BRECKNER W.W.: Cercetare operationala, Univ.Babes-Bolyai, Cluj-Napoca ,1981.
3. BRECKNER W.W.: DUCA D.I.: Culegere de probleme de cercetare operationala, Universitatea, Cluj-Napoca, 1983.
4. FORGO F.: Nonconvex programming. Budapest: Akademiai Kiado, 1988.
5. JONGEN H.Th., MEER K., TRIESCH E.: Optimization Theory, New York, Boston, Dordrecht, London, Moscow: Kluwer Academic Publishers, 2004
6. LUPSA L.: Numerical optimization methods. Special issues in discrete optimization. Cluj-Napoca: Risoprint, 2005
7. NOCEDAL J., WRIGHT S.J.: Numerical Optimization, Second Edition, New York: Springer, 2006
8. PADBERG M.: Linear Optimization and Extensions, Springer-Verlag,Berlin, 1995
9. PANIK M.J.: Linear Programming: mathematics, theory and algorithms, Kluwer Academic Publishers, Dordrecht, 1996.
10. VOSE M.D., The simple Genetic Algorithm: Foundations and Theory. Cambrige: MIT Press,MA, 1998
Assessment
Exam and Prezentation.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject