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

SUBJECT

Code
Subject
MMA1012 Optimization Models
Section
Semester
Hours: C+S+L
Category
Type
Component-Based Programming - in English
2
2+2+0
speciality
compulsory
Teaching Staff in Charge
Assoc.Prof. POPOVICI Nicolae, Ph.D.,  popovicimath.ubbcluj.ro
Aims
The aim of this course is to present several classical and modern optimization models, from both theoretical and practical points of view.
Content
Special instances of linear optimization: resource allocation problems, diet problems; integer programming (Gomory method); multicriteria linear optimization with respect to domination or lexicographic ordering; transportation problems. Nonlinear optimization models; numerical methods for solving unconstrained or constrained optimization problems (gradient methods, penalty and barrier functions methods). Dynamic programming models: the Bellman’s principle of dynamic programming; applications of its continuous and discrete versions to economics and network-type problems. Optimization models via calculus of variations: the fundamental problem of the calculus of variations; the Euler equation and some of its special cases; transversality conditions; applications.
References
1. ANDERSON, D.R., SWEENEY, D.J., WILLIAMS, T.A., An Introduction to Management Science. Quantitative Approaches to Decision Making, South-Western College Publishing, Cincinnati, 2000.
2. BRECKNER, B.E., POPOVICI, N.: Probleme de cercetare operaţională, EFES, Cluj-Napoca, 2006.
3. BRECKNER, W.W.: Cercetare operationala, Universitatea $Babes-Bolyai$, Facultatea de Matematica, Cluj-Napoca, 1981.
4. CHIANG, A.C.: Elements of Dynamic Optimization. McGraw-Hill, New York, 1992.
5. DACOROGNA, B.: Introduction au calcul des variations. Presses Polytechniques et Universitaires Romandes, Laussane, 1992.
6. EHRGOT, M.: Multicriteria Optimization. Springer, Berlin Heidelberg New York, 2005.
7. HILLERMEIER, C.: Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach. Birkhauser Verlag, Basel - Boston - Berlin, 2001.
8. POPOVICI, N.: Optimizare vectoriala, Casa Cartii de Stiinta, Cluj-Napoca, 2005.
9. STEFANESCU, A., ZIDAROIU, C.: Cercetari operationale, Editura Didactica si Pedagogica, Bucuresti, 1981.
10. VANDERBEI, R.: Linear Programming. Foundations and Extensions, Springer, New York, 2008.
Assessment
Continuous evaluation (contributes 20% to the assesment), written and oral exam (contributes 80% to the assesment).
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject