Overcoming the failure of the classical generalized interior-point regularity conditions in convex optimization [Elektronische Ressource] : applications of the duality theory to enlargements of maximal monotone operators / vorgelegt von Ernö Robert Csetnek

Overcoming the failure of theclassical generalized interior-pointregularity conditions in convexoptimization. Applications of theduality theory to enlargements ofmaximal monotone operatorsVon der Fakult at fur Mathematik der Technischen Universit at ChemnitzgenehmigteD i s s e r t a t i o nzur Erlangung des akademischen GradesDoctor rerum naturalium(Dr. rer. nat.)vorgelegt vonDipl. - Math. Ern o Robert Csetnekgeboren am 18.03.1981 in Satu Mare (Rum anien)eingereicht am 02.07.2009Gutachter: Prof. Dr. Gert WankaProf. Dr. Heinz H. BauschkeProf. Dr. Marco A. L opez Cerd aTag der Verteidigung: 08.12.2009Bibliographical descriptionErn o Robert CsetnekOvercoming the failure of the classical generalized interior-point reg-ularity conditions in convex optimization. Applications of the dualitytheory to enlargements of maximal monotone operatorsDissertation, 110 pages, Chemnitz University of Technology, Faculty of Mathe-matics, 2009ReportThe aim of this work is to present several new results concerning duality inscalar convex optimization, the formulation of sequential optimality conditions andsome applications of the duality to the theory of maximal monotone operators.After recalling some properties of the classical generalized interiority notionswhich exist in the literature, we give some properties of the quasi interior andquasi-relative interior, respectively.