Duality for convex composed programming problems [Elektronische Ressource] / vorgelegt von Emese Tünde Vargyas

Duality for convex composedprogramming problemsVon derFakult 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.)vorgelegtvonDipl.-Math. Emese Tunde Vargyasgeboren am 21.02.1975 in Reghin (Rum anien)eingereicht am: 05.07.2004Gutachter: Prof. Dr. Gert WankaProf. Dr. Kathrin KlamrothConf. Dr. G abor KassayTag der Verteidigung: 25.11.2004Bibliographical descriptionEmese Tunde VargyasDuality for convex composed programming problemsDissertation, 102 pages, Chemnitz University of Technology, Faculty of Math-ematics, 2004ReportThe theory of duality represents an important research area in optimization.The goal of this work is to present a conjugate duality treatment of composedprogramming as well as to give an overview of some recent developments in bothscalar and multiobjective optimization.In order to do this, rst we study a single-objective optimization problem, inwhich the objective function as well as the constraints are given by composedfunctions. By means of the conjugacy approach based on the perturbation the-ory, we provide di eren t kinds of dual problems to it and examine the relationsbetween the optimal objective values of the duals. Given some additional as-sumptions, we verify the equality between the optimal objective values of theduals and strong duality between the primal and the dual problems, respectively.