A coarse solution of generalized semi-infinite optimization problems via robust analysis of marginal functions and global optimization [Elektronische Ressource] / vorgelegt von Abebe Geletu W. Selassie

ACOARSESOLUTIONOFGENERALIZEDSEMI-INFINITEOPTIMIZATIONPROBLEMSVIAROBUSTANALYSISOFMARGINALFUNCTIONSANDGLOBALOPTIMIZATION.vorgelegt vonDipl.-Math. Abebe Geletu W. SelassieDISSERTATIONzur Erlangung des akademischen GradesDr. rer. nat.Eingereicht bei der Technischen Universit¨at IlmenauJuni, 2004Tag der wissenschaftlichen Aussprache: 17.12.20041. Gutachter: Prof. Dr. rer. nat. habil. Armin Hoffmann.2. Gutachter: Prof. Dr. rer. nat. habil. Gerhard-Wilhelm Weber3. Gutachter: Prof. Dr. rer. nat. habil. Rainer Tichatschkeurn:nbn:de:gbv:ilm1-2004000167March 22, 2005To my wife Genet, and my son Abenezer and my daughterBethel whose love, patience and understanding carried me sofar.March 22, 2005Table of ContentsTable of Contents iv1 Facts from Set-Valued Analysis 81.1 Set-Valued Maps - General Definitions and Properties . . . . . . . . . . . . 91.2 Set-Valued Maps with given Structures . . . . . . . . . . . . . . . . . . . . 131.2.1 Regularity Conditions and their Consequences . . . . . . . . . . . . 161.2.2 Constraint Qualifications and their Consequences . . . . . . . . . . 192 A Review of Generalized Semi-infinite Optimization 232.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2 Structure of the Feasible Set . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2.1 Global Structure of the Feasible Set . . . . . . . . . . . . . . . . . . 272.2.2 Disjunctive Structures in GSIP . . . . . . . . . . . . . . . . . . .