Universitatea "Babes-Bolyai" Cluj-Napoca
Facultatea de Matematica si Informatica
FISA DISCIPLINEI

Analiză nenetedă
Cod
Semes-
trul
Ore: C+S+L
Credite
Tipul
Sectia
MO033
7
2+2+0
6
optionala
Matematică-Informatică
Cadre didactice indrumatoare
Prof. Dr. MURESAN Marian, mmarian@math.ubbcluj.ro
Obiective
Formarea si dezvoltarea abilitatii studentilor de a aborda probleme de optimizare cu date nenetede.
Continut
1. Introducere
1.1. Exemple de probleme de optimizare avand date nederivabile
2.1. Penalitati si restrictii
2. Multifunctii
2.1. Convergente de multimi
2.2. Notiuni de masurabilitate, teoreme de selectie
3. Subgradienti
3.1. Definitii si proprietati de baza
3.2. Legatura cu derivatele si subderivatele
3.2. Reguli de calcul
3.3. Conuri: Clarke, Bouligand, intermediar, Ioffe, Mordukhovich
4. Geometria analizei nenetede
4.1. Principii variationale
4.2. Normale proximale si subgradienti proximali
4.3. Normale proximinale la limita si subgradienti proximali la limita
4.4. Dualitate
5. Calculul subdiferential
5.1. Reguli de calcul
5.2. Regula generalizata a multiplicatorilor lui Lagrange si aplicatii
6. Aplicatii
6.1. Metoda arcului adjunct in optimizarea neneteda
6.2. Aplicatii in economie, puncte de echilibru
6.3. Aplicatii in inginerie
Bibliografie
1. Choset, H., Nonsmooth analysis, convex analysis, and their applications to motion planning, Intern. J. Comp. Geo. Appl., vol. 9(1999), nr. 4-5, 447-467.
2. Clarke, F. H., Optimization and Nonsmooth Analysis, SIAM, Philadelphia, 1990.
3. Jofre, A., A second-welfare theorem in non-convex economies, Canad. Math. J., vol. 27(2000), 175-184.
4. Loewen, P. D., Optimal Control and Nonsmooth Analysis, AMS, Providence, 1993.
5. Loewen, P. D., Rockafellar, T. R., The adjoint arc in nonsmooth optimization, SIAM J. Control Optim., 325(1991), 39-72.
6. Khan, M. A., Ioffe's normal cone and the foundations of welfare economics: the infinite dimensional theory, J. Math. Anal. Appl., vol. 161(1991), 284-298.
7. Mordukhovich, B., The extremal principle and its applications to optimixation and economics, in Optimization and related topics (A. Rubinov and B. Glover, eds.) Applied Optimization, vol. 47, Kluwer, 343-369.
8. Muresan, M., Analiza neneteda, Risoprint, Cluj-Napoca, 2001.
9. Rockafellar, T. R., Wets, R. J.-B., Variational Analysis, Springer, New York, 1998.
Evaluare
Un referat si un examen oral.