Analiză nenetedă | Non-smooth analysis |
trul |
|||||
(Mathematics) |
Cadre didactice indrumatoare | Teaching Staff in Charge |
Conf. Dr. MURESAN Marian, mmarian@math.ubbcluj.ro |
Obiective | Aims |
Formarea si dezvoltarea abilitatii studentilor de a aborda probleme de optimizare cu date nenetede. |
Training up and improving the students' skill to deal with optimization problems with nonsmooth data. |
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 3. Gradienti generalizati 3.1. Definitie si proprietati de baza 3.2. Legatura cu derivatele si subderivatele 3.2. Reguli de calcul 3.3. Conuri: Clarke, Bouligand, intermediar 4. Geometria analizei nenetede 4.1. Normale proximinale si subgradienti 4.2. Normale limitatoare si subgradienti 4.3. Dualitate 5. Calculul subdiferential 5.1. Reguli de calcul 5.2. Integrarea gradientilor proximinali. Regula generalizata a multiplicatorilor lui Lagrange 6. Aplicatii in programarea neneteda 6.1. Metoda arcului adjunct in optimizarea neneteda |
1. Clarke, F. H., Optimization and Nonsmooth Analysis, SIAM, Philadelphia, 1990.
2. Loewen, P. D., Optimal Control and Nonsmooth Analysis, AMS, Providence, 1993. 3. Loewen, P. D., Rockafellar, T. R., The adjoint arc in nonsmooth optimization, SIAM J. Control Optim., 325(1991), 39-72. 4. Mordukhovich, B., Optimal control of nonconvex discrete and differential inclusions, Proc. 3rd Inter. Conf. Appox. & Optim. at the Caribbean, 1997. 5. Muresan, M., An Introduction to Set-valued Analysis, ELTE, Budapest, 1997. 6. Rockafellar, T. R., Wets, R. J.-B., Variational Analysis, Springer, New York, 1998. |
Evaluare | Assessment |
Un referat si un examen oral. |
A review and an exam. |