Faculty of Mathematics and Computer Science

Convex analysis |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

Teaching Staff in Charge |

Assoc.Prof. KASSAY Gabor, Ph.D., kassay@math.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. J.P.Aubin: Optima and Equilibria: An Introduction to Nonliniar Analysis, Springer-Verlag, Berlin Heidelberg, 1993
2. J.P.Aubin, I.Ekeland: Applied Nonliniar Analysis, John Wiley and Sohns, 1984 3. V. Barbu, T.Precupanu: Convexity and Optimization in Banach Spaces, Publ.House of Roum. Acad. and Reidel Publishing Comp.,1986 4. L.Danzer, B. Grunbaum, V.Klee: Helly's Theorem and its Relatives, Convexity, Proceedings of Symposia in Pure Mathematics, vol VII, A.M.S.,Providence, Rhode Island, 1963 5. J.-B.Hiriart-Urruty, C. Lemarechal: Convex Analysis and Minimization Algoritms, I,II,Springer-Verlag, Berlin Heidelberg, 1993 6. R. Holmes: Geometric Functional Analysis and its Applicatons, Springer Verlag, Berlin, 1975 7. J. Kolumban: Convex Analysis , I, Babes-Bolyai University Cluj-Napoca, 1997 8. T. Precupanu: Spatii liniare topologice si elemente de analiza convexa, Ed. Acad. Romane, 1992 8. R.T.Rockafellar: Convex Analysis, Princepton Univ.Press,1970 |

Assessment |