A duality approach to gap functions for variational inequalities and equilibrium problems [Elektronische Ressource] / vorgelegt von Lkhamsuren Altangerel

A duality approachto gap functions for variationalinequalities and equilibriumproblemsVon der Fakult¨at fur¨ Mathematikder Technischen Universit¨at Chemnitz genehmigteD i s s e r t a t i o nzur Erlangung des akademischen GradesDoctor rerum naturalium(Dr. rer. nat.)vorgelegt vonM.Sc. Lkhamsuren Altangerelgeboren am 22.06.1974 in Khovd (Mongolei)eingereicht am 12.04.2006Gutachter: Prof. Dr. Gert WankaProf. Dr. Petra WeidnerProf. Dr. Rentsen EnkhbatTag der Verteidigung: 25.07.2006To my parentsBibliographical descriptionLkhamsuren AltangerelA duality approach to gap functions for variational inequalities and equi-librium problemsDissertation, 112 pages, Chemnitz University of Technology, Faculty ofMathematics, Chemnitz, 2006.AbstractThis work aims to investigate some applications of the conjugate duality for scalarand vector optimization problems to the construction of gap functions for varia-tional inequalities and equilibrium problems. The basic idea of the approach isto reformulate variational inequalities and equilibrium problems into optimizationproblems depending on a fixed variable, which allows us to apply duality resultsfrom optimization problems.Based on some perturbations, first we consider the conjugate duality for scalaroptimization. As applications, duality investigations for the convex partially sepa-rable optimization problem are discussed.