"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Convex analysis
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MO259
1
2+1+1
8
compulsory
Analiză Reală şi Complexă - în limba engleză
Teaching Staff in Charge
Lect. POPOVICI Nicolae, Ph.D.,  popovicimath.ubbcluj.ro
Aims
Getting some knowledges in convex analysis, especially those considered to be essential in the education of students at the post-graduate level.
Content
Algebraic properties of convex sets, algebraic properties of convex and quasiconvex functions. Topological properties of convex sets, topological properties of convex and quasiconvex functions. Dual representation of convex and quasiconvex functions. Applications: minimax theorems and game theory, duality theory in optimization.
References
1. AUBIN J. P.: Optima and Equilibria: An Introduction to Nonlinear Analysis. Berlin - Heidelberg: Springer-Verlag, 1993.
2. AUBIN J. P., EKELAND I.: Applied Nonlinear Analysis. New York: John Wiley and Sons, 1984.
3. BARBU V., PRECUPANU T.: Convexity and Optimization in Banach Spaces. Bucuresti: Publ. House of Roum. Acad. and Reidel Publishing Comp., 1986.
4. DANZER L., GRÜNBAUM B., KLEE V.: Helly's Theorem and its Relatives. Convexity. Proceedings of Symposia in Pure Mathematics. VII. Providence: A.M.S., 1963.
5. HIRIART-URRUTY J.-B., LEMARÉCHAL C.: Convex Analysis and Minimization Algorithms. I, II. Berlin - Heidelberg - New York: Springer-Verlag, 1993.
6. HOLMES R. B.: Geometric Functional Analysis. Berlin: Springer-Verlag, 1975.
7. KOLUMBÁN J.: Convex Analysis. I. Cluj-Napoca: Babes-Bolyai University, 1997.
8. PRECUPANU T.: Spatii liniare topologice si elemente de analiza convexa. Bucuresti: Editura Academiei Române, 1992.
9. ROCKAFELLAR R. T.: Convex Analysis. Princeton: Princeton University Press, 1970.
Assessment