Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Matematica
Programul de studii: Algebră şi Geometrie (în limba engleză)
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MO267	Special Topics in Modern Mathematics (2)	

Semester	Hours: C+S+L	Category	Status	
2	2+2+0		compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
MODOI Gheorghe Ciprian	Ph.D.	Lect.	Algebra	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
Students will learn the methods and techniques of optimization theory.	

IV. Course contents
1. Convex Analysis in Complex Space
  1.1 Convex Sets
  1.2 Separation Theorems for Convex Sets
  1.3 Cones
  1.4 The Polar of a Set
  1.5 Theorems of the Alternative
  1.6 Convex Functions and Generalizations of Convex Functions

2. Optimization in Complex Space
  2.1  Optimization Problems in Complex Space
  2.2  Necessary Optimality Criteria and Sufficient Optimality Criteria
  2.3  Necessary Optimality Criteria with Differentiable Hypotheses about the Functions
  2.4  Sufficient Optimality Criteria with Differentiable Hypotheses about the Functions
  2.5  Linearization Properties of the Optimization Problem

3. Multicriteria Optimization in Complex Space
  3.1 Efficient Points, Weakly Efficient Points, Ideal Points
  3.2 The Structure of the Set of Efficient Points
  3.3 Multicriteria Optimization Problems in Complex Space
  3.4 Necessary Efficieny Criteria
  3.5 Sufficient Efficiency Criteria
  3.6 Properly Efficiency in the Multicriteria Optimization

V. Bibliography
1. J.-P. AUBIN: Optima and Equilibria. An Introduction to Nonlinear Analysis, Springer-Verlag, Berlin/Heidelberg 1993
2. J.-P. AUBIN and I. EKELAND: Applied Nonlinear Analysis, John Wiley and Sons, New York, 1984
3. D.I. DUCA: Multicriteria Optimization in Complex Space, Casa Cartii de Stiinta, Cluj-Napoca, 2005 
4. D.I. DUCA: Optimization in Complex Space (in romanian), Ed. GIL, Zalau, 2002 
5. C. ZALINESCU: Programare matematica in spatii normate infinit dimensionale, Ed. Academiei Romane, Bucuresti, 1998

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Homeworks. Essays. Exam.	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Lect. MODOI Gheorghe Ciprian, Ph.D.