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

Code	Subject	
MMA1012	Optimization Models	

Section	Sem.	Hours: C+S+L	Category	Type	
Component-Based Programming - in English	2	2+1+0	speciality	compulsory	

Teaching Staff in Charge	Assoc.Prof. POPOVICI Nicolae, Ph.D., popovici@math.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&#8217;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.	
Bibliography	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).