Leung, Ka Lun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 118-126). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Constraint Satisfaction and Global Constraints --- p.3 / Chapter 1.2 --- Soft Constraints --- p.4 / Chapter 1.3 --- Motivation and Goal --- p.5 / Chapter 1.4 --- Outline of the Thesis --- p.6 / Chapter 2 --- Background --- p.8 / Chapter 2.1 --- Constraint Satisfaction Problems --- p.8 / Chapter 2.1.1 --- Backtracking Tree Search --- p.10 / Chapter 2.1.2 --- Local Consistency in CSP --- p.11 / Chapter 2.1.3 --- Constraint Optimization Problem --- p.16 / Chapter 2.2 --- Weighted Constraint Satisfaction --- p.21 / Chapter 2.2.1 --- Branch and Bound Search --- p.23 / Chapter 2.2.2 --- Local Consistency in WCSP --- p.26 / Chapter 2.3 --- Global Constraints --- p.35 / Chapter 2.4 --- Flow Theory --- p.37 / Chapter 3 --- Related Work --- p.39 / Chapter 3.1 --- Handling Soft Constraints in COPs --- p.39 / Chapter 3.2 --- Global Constraints --- p.40 / Chapter 3.2.1 --- Hard Global Constraints --- p.40 / Chapter 3.2.2 --- Soft Global Constraints --- p.41 / Chapter 3.3 --- Local Consistency in Weighted CSP --- p.42 / Chapter 4 --- “Soft as Hard´ح Approach --- p.44 / Chapter 4.1 --- The General “Soft as Hard´ح Approach --- p.44 / Chapter 4.2 --- Cost-based GAC --- p.49 / Chapter 4.3 --- Empirical Results --- p.53 / Chapter 5 --- Weighted CSP Approach --- p.55 / Chapter 5.1 --- Strong 0-Inverse Consistency --- p.55 / Chapter 5.1.1 --- 0-Inverse Consistency and Strong 0-Inverse Consistency --- p.56 / Chapter 5.1.2 --- Comparison with Other Consistencies --- p.62 / Chapter 5.2 --- Generalized Arc Consistency Star --- p.65 / Chapter 5.3 --- Full Directional Generalized Arc Consistency Star --- p.72 / Chapter 5.4 --- Generalizing EDAC* --- p.78 / Chapter 5.5 --- Implementation Issues --- p.87 / Chapter 6 --- Towards A Library of Efficient Soft Global Constraints --- p.90 / Chapter 6.1 --- The allDifferent Constraint --- p.91 / Chapter 6.1.1 --- All Interval Series --- p.93 / Chapter 6.1.2 --- Latin Square --- p.95 / Chapter 6.2 --- The GCC Constraint --- p.97 / Chapter 6.2.1 --- Latin Square --- p.100 / Chapter 6.2.2 --- Round Robin Tournament --- p.100 / Chapter 6.3 --- The Same Constraint --- p.102 / Chapter 6.3.1 --- Fair Scheduling --- p.104 / Chapter 6.3.2 --- People-Mission Scheduling --- p.105 / Chapter 6.4 --- The Regular Constraint --- p.106 / Chapter 6.4.1 --- Nurse Rostering Problem --- p.110 / Chapter 6.4.2 --- Modelling Stretch() Constraint --- p.111 / Chapter 6.5 --- Discussion --- p.113 / Chapter 7 --- Conclusion and Remarks --- p.115 / Chapter 7.1 --- Contributions --- p.115 / Chapter 7.2 --- Future Work --- p.117 / Bibliography --- p.118

Thesis (Ph.D.)--University of Delaware, 2009. / Principal faculty advisor: Keith S. Decker, Dept. of Computer & Information Sciences. Includes bibliographical references.

Jiang, Kening. / "August 2011." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 90-93). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Portfolio Selection Using Clustering Methodology --- p.7 / Chapter 2.1 --- Heuristic algorithm --- p.8 / Chapter 2.1.1 --- Step 1: Security transformation by factor model --- p.8 / Chapter 2.1.2 --- Step 2: Clustering algorithm --- p.10 / Chapter 2.1.3 --- Step 3: Representative selection by t he Sliarpe ratio --- p.16 / Chapter 2.2 --- Numerical results --- p.17 / Chapter 3 --- Modified Portfolio Selection Using Clustering Methodology --- p.22 / Chapter 3.1 --- Analysis of artificial factors --- p.23 / Chapter 3.2 --- Problem reformulation --- p.27 / Chapter 3.3 --- Numerical results --- p.29 / Chapter 4 --- Minimum Variance Point --- p.70 / Chapter 4.1 --- Iterative elimination scheme I --- p.72 / Chapter 4.2 --- Iterative elimination scheme II --- p.74 / Chapter 4.3 --- Orthogonal matrix mapping --- p.76 / Chapter 4.4 --- Condition to solve diagonal dominant problem --- p.77 / Chapter 4.5 --- L1 formulation --- p.82 / Chapter 4.6 --- Numerical results --- p.85 / Chapter 5 --- Summary and Future work --- p.88

Optical signal-to-noise ratio (OSNR) is considered as the dominant performance parameter at the physical layer in optical networks. This thesis is interested in control and optimization of channel OSNR by using optimization and game-theoretic approaches, incorporating two physical constraints: the link capacity constraint and the channel OSNR target. To start, we study OSNR optimization problems with link capacity constraints in single point-to-point fiber links via two approaches. We first present a framework of a Nash game between channels towards optimizing individual channel OSNR. The link capacity constraint is imposed as a penalty term to each cost function. The selfish behavior in a Nash game degrades the system performance and leads to the inefficiency of Nash equilibria. From the system point of view, we formulate a system optimization problem with the objectives of achieving an OSNR target for each channel while satisfying the link capacity constraint. As an alternative to study the efficiency of Nash equilibria, we use the system framework to investigate the effects of parameters in cost functions in the game-theoretic framework. Then extensions to multi-link and mesh topologies are carried out. We propose a partition approach by using the flexibility of channel power adjustment at optical switches. The multi-link structure is partitioned into stages with each stage being a single sink. By fully using the flexibility, a more natural partition approach is applied to mesh topologies where each stage is a single link. The closed loop in mesh topologies can be unfolded by selecting a starting link. Thus instead of maximization of channel OSNR from end to end, we consider minimization of channel OSNR degradation between stages. We formulate a partitioned Nash game which is composed of ladder-nested stage Nash games. Distributed algorithms towards the computation of a Nash equilibrium solution are developed for all different game frameworks. Simulations and experimental implementations provide results to validate the applicability of theoretical results.

Optical signal-to-noise ratio (OSNR) is considered as the dominant performance parameter at the physical layer in optical networks. This thesis is interested in control and optimization of channel OSNR by using optimization and game-theoretic approaches, incorporating two physical constraints: the link capacity constraint and the channel OSNR target. To start, we study OSNR optimization problems with link capacity constraints in single point-to-point fiber links via two approaches. We first present a framework of a Nash game between channels towards optimizing individual channel OSNR. The link capacity constraint is imposed as a penalty term to each cost function. The selfish behavior in a Nash game degrades the system performance and leads to the inefficiency of Nash equilibria. From the system point of view, we formulate a system optimization problem with the objectives of achieving an OSNR target for each channel while satisfying the link capacity constraint. As an alternative to study the efficiency of Nash equilibria, we use the system framework to investigate the effects of parameters in cost functions in the game-theoretic framework. Then extensions to multi-link and mesh topologies are carried out. We propose a partition approach by using the flexibility of channel power adjustment at optical switches. The multi-link structure is partitioned into stages with each stage being a single sink. By fully using the flexibility, a more natural partition approach is applied to mesh topologies where each stage is a single link. The closed loop in mesh topologies can be unfolded by selecting a starting link. Thus instead of maximization of channel OSNR from end to end, we consider minimization of channel OSNR degradation between stages. We formulate a partitioned Nash game which is composed of ladder-nested stage Nash games. Distributed algorithms towards the computation of a Nash equilibrium solution are developed for all different game frameworks. Simulations and experimental implementations provide results to validate the applicability of theoretical results.

No description available.

No description available.

The primary aim of this study is to assess the applicability and performance of the finite element method (FEM) in solving structural optimization problems with stability constraints. In order to reach this goal, several optimization problems are solved using FEM which are briefly described as follows: The strongest column problem is one of the oldest optimization problems for which analytical solutions exist only for some special cases. Here, both unimodal and bimodal optimization of columns under concentrated and/or distributed compressive loads with several different boundary conditions and constraints are performed using an iterative method based on finite elements. The analytical solutions available in the literature for columns under concentrated loads and an analytical solution derived for simply supported columns under distributed loads are used for verification purposes. Optimization results are presented for fibre-reinforced composite rectangular plates under inplane loads. The non-uniformity of the in-plane stresses due to stress diffusion and/or in-plane boundary conditions is taken into account, and its influence on optimal buckling load is investigated. It is shown that the exclusion of the in-plane restraints may lead to errors in stability calculations and consequently in optimal design. The influences of the panel aspect ratio, stacking sequence, panel thickness, and the rotational edge restraints on the optimal axially compressed cylindrical and non-cylindrical curved panels are investigated, where the optimal panel is the one with the highest failure load. The prebuckling and the first-ply failure loads of the panels are calculated and minimum of these two is selected as the failure load. The results show that there are distinct differences between the behaviour of cylindrical and non-cylindrical panels. The formulations of the finite elements which are used throughout the study are given and several verification problems are solved to verify the accuracy of the methodology. The computer codes written in Matlab are also given in the appendix sections accompanied with the selected codes used for optimization purposes. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2006.

Thesis (M.S.)--Oregon State University, 2008. / Printout. Includes bibliographical references (leaves 62-64). Also available on the World Wide Web.

This thesis is concerned with a certain class of algorithms for the solution of constrained optimization problems and generalized Nash equilibrium problems in Hilbert spaces. This class of algorithms is inspired by the alternating direction method of multipliers (ADMM) and eliminates the constraints using an augmented Lagrangian approach. The alternating direction method consists of splitting the augmented Lagrangian subproblem into smaller and more easily manageable parts. Before the algorithms are discussed, a substantial amount of background material, including the theory of Banach and Hilbert spaces, fixed-point iterations as well as convex and monotone set-valued analysis, is presented. Thereafter, certain optimization problems and generalized Nash equilibrium problems are reformulated and analyzed using variational inequalities and set-valued mappings. The analysis of the algorithms developed in the course of this thesis is rooted in these reformulations as variational inequalities and set-valued mappings. The first algorithms discussed and analyzed are one weakly and one strongly convergent ADMM-type algorithm for convex, linearly constrained optimization. By equipping the associated Hilbert space with the correct weighted scalar product, the analysis of these two methods is accomplished using the proximal point method and the Halpern method. The rest of the thesis is concerned with the development and analysis of ADMM-type algorithms for generalized Nash equilibrium problems that jointly share a linear equality constraint. The first class of these algorithms is completely parallelizable and uses a forward-backward idea for the analysis, whereas the second class of algorithms can be interpreted as a direct extension of the classical ADMM-method to generalized Nash equilibrium problems. At the end of this thesis, the numerical behavior of the discussed algorithms is demonstrated on a collection of examples. / Die vorliegende Arbeit behandelt eine Klasse von Algorithmen zur Lösung restringierter Optimierungsprobleme und verallgemeinerter Nash-Gleichgewichtsprobleme in Hilberträumen. Diese Klasse von Algorithmen ist angelehnt an die Alternating Direction Method of Multipliers (ADMM) und eliminiert die Nebenbedingungen durch einen Augmented-Lagrangian-Ansatz. Im Rahmen dessen wird in der Alternating Direction Method of Multipliers das jeweilige Augmented-Lagrangian-Teilproblem in kleinere Teilprobleme aufgespaltet. Zur Vorbereitung wird eine Vielzahl grundlegender Resultate präsentiert. Dies beinhaltet entsprechende Ergebnisse aus der Literatur zu der Theorie von Banach- und Hilberträumen, Fixpunktmethoden sowie konvexer und monotoner mengenwertiger Analysis. Im Anschluss werden gewisse Optimierungsprobleme sowie verallgemeinerte Nash-Gleichgewichtsprobleme als Variationsungleichungen und Inklusionen mit mengenwertigen Operatoren formuliert und analysiert. Die Analysis der im Rahmen dieser Arbeit entwickelten Algorithmen bezieht sich auf diese Reformulierungen als Variationsungleichungen und Inklusionsprobleme. Zuerst werden ein schwach und ein stark konvergenter paralleler ADMM-Algorithmus zur Lösung von separablen Optimierungsaufgaben mit linearen Gleichheitsnebenbedingungen präsentiert und analysiert. Durch die Ausstattung des zugehörigen Hilbertraums mit dem richtigen gewichteten Skalarprodukt gelingt die Analyse dieser beiden Methoden mit Hilfe der Proximalpunktmethode und der Halpern-Methode. Der Rest der Arbeit beschäftigt sich mit Algorithmen für verallgemeinerte Nash-Gleichgewichtsprobleme, die gemeinsame lineare Gleichheitsnebenbedingungen besitzen. Die erste Klasse von Algorithmen ist vollständig parallelisierbar und es wird ein Forward-Backward-Ansatz für die Analyse genutzt. Die zweite Klasse von Algorithmen kann hingegen als direkte Erweiterung des klassischen ADMM-Verfahrens auf verallgemeinerte Nash-Gleichgewichtsprobleme aufgefasst werden. Abschließend wird das Konvergenzverhalten der entwickelten Algorithmen an einer Sammlung von Beispielen demonstriert.