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

Code	Subject	
MO267	Special Topics in Modern Mathematics (2)	

Section	Semester	Hours: C+S+L	Category	Type	
Algebra and Geometry - in English	2	2+2+0		compulsory	
Real and Compex Analysis - in English	2	2+2+0		compulsory	

Teaching Staff in Charge	Prof. DUCA Dorel, Ph.D., dduca@math.ubbcluj.ro	
Aims	Students will learn the methods and techniques of optimization theory.	
Content	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

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
	
Assessment	Homeworks. Essays. Exam.