Universiẗat, Diss., 2000--Dortmund.

Techn. Universiẗat, Diss., 2004--Berlin.

Techn. Hochsch., Diss., 2005--Aachen.

The subject of this thesis are mathematical programs with complementarity conditions (MPCC). At first, an economic example of this problem class is analyzed, the problem of effort maximization in asymmetric n-person contest games. While an analytical solution for this special problem could be derived, this is not possible in general for MPCCs. Therefore, optimality conditions which might be used for numerical approaches where considered next. More precisely, a Fritz-John result for MPCCs with stronger properties than those known so far was derived together with some new constraint qualifications and subsequently used to prove an exact penalty result. Finally, to solve MPCCs numerically, the so called relaxation approach was used. Besides improving the results for existing relaxation methods, a new relaxation with strong convergence properties was suggested and a numerical comparison of all methods based on the MacMPEC collection conducted. / Das Thema dieser Dissertation sind mathematische Programme mit Komplementaritätsrestriktionen (MPCC). Zunächst wurde eine ökonomische Anwendung dieses Problemklasse betrachtet, das sogenannte Wettbewerbsdesignproblem. Während es für dieses spezielle Problem möglich war eine analytische Lösung herzuleiten, ist dies im Allgemeinen nicht möglich. Daher wurden anschließend Optimalitätsbedingungen, die für eine numerische Lösung verwendet werden können, betrachtet. Genauer wurde ein stärkeres Fritz-John Resultat als die bisher bekannten zusammen mit neuen Constraint Qualifications hergeleitet und anschließend zum Beweis eines exakten Penaltyresultates benutzt. Schließlich wurden zur numerischen Lösung von MPCCs sogenannte Relaxationsverfahren betrachtet. Zusätzlich zur Verbesserung der Resultate für bekannte Verfahren wurde eine neue Relaxierung mit starken Konvergenzeigenschaften vorgeschlagen und ein numerischer Vergleich aller Verfahren auf Basis der MacMPEC Testsammlung durchgeführt.

Univ., Diss.--Pisa, 2003.

University, Diss., 2002--Saarbrücken.

University, Diss., 1998--Saarbrücken.

A constraint is a formula in first-order logic expressing a relation between values of various domains. In order to solve a constraint, constructing a propositional encoding is a successfully applied technique that benefits from substantial progress made in the development of modern SAT solvers. However, propositional encodings are generally created by developing a problem-specific generator program or by crafting them manually, which often is a time-consuming and error-prone process especially for constraints over complex domains. Therefore, the present thesis introduces the constraint solver CO4 that automatically generates propositional encodings for constraints over structured finite domains written in a syntactical subset of the functional programming language Haskell. This subset of Haskell enables the specification of expressive and concise constraints by supporting user-defined algebraic data types, pattern matching, and polymorphic types, as well as higher-order and recursive functions. The constraint solver CO4 transforms a constraint written in this high-level language into a propositional formula. After an external SAT solver determined a satisfying assignment for the variables in the generated formula, a solution in the domain of discourse is derived. This approach is even applicable for finite restrictions of recursively defined algebraic data types. The present thesis describes all aspects of CO4 in detail: the language used for specifying constraints, the solving process and its correctness, as well as exemplary applications of CO4.

Diese Arbeit befasst sich mit der Entwicklung einer Applikation, welche Infrastrukturdaten über Eisenbahnnetze generiert. Dabei bildet die Erzeugung der topologischen Informationen den Schwerpunkt dieser Arbeit. Der Anwender charakterisiert hierfür vorab das gewünschte Eisenbahnnetz, wobei die geforderten Eigenschaften die Randbedingungen darstellen, die bei der Synthese zu beachten sind. Zur Einhaltung dieser Bedingungen wird die Constraint-Programmierung eingesetzt, welche durch ihr spezielles Programmierparadigma konsistente Lösungen effizient erzeugt. Dies wird u.a. durch die Nachnutzung so genannter globaler Constraints erreicht. Aus diesem Grund wird insbesondere auf den Einsatz der Constraint-Programmierung bei der Modellierung und Implementierung der Applikation eingegangen. / This work deals with the development of an application, which generates infrastructure data of railway networks. The focus of this work concentrates on the generation process of topological information. As input for the application a characterization of the intended railway network is given as attributes, which are handled as constraints in the generation process. To satisfy these restrictions constraint programming, a special programming paradigm, which is able to search efficently consistent solutions, is applied. In particular, the use of so-called global constraints improves the computation. For that reason the role of constraint-programming in modelling and implementing these application is discussed in more detail.

A constraint is a formula in first-order logic expressing a relation between values of various domains. In order to solve a constraint, constructing a propositional encoding is a successfully applied technique that benefits from substantial progress made in the development of modern SAT solvers. However, propositional encodings are generally created by developing a problem-specific generator program or by crafting them manually, which often is a time-consuming and error-prone process especially for constraints over complex domains. Therefore, the present thesis introduces the constraint solver CO4 that automatically generates propositional encodings for constraints over structured finite domains written in a syntactical subset of the functional programming language Haskell. This subset of Haskell enables the specification of expressive and concise constraints by supporting user-defined algebraic data types, pattern matching, and polymorphic types, as well as higher-order and recursive functions. The constraint solver CO4 transforms a constraint written in this high-level language into a propositional formula. After an external SAT solver determined a satisfying assignment for the variables in the generated formula, a solution in the domain of discourse is derived. This approach is even applicable for finite restrictions of recursively defined algebraic data types. The present thesis describes all aspects of CO4 in detail: the language used for specifying constraints, the solving process and its correctness, as well as exemplary applications of CO4.