Dissertations / Theses: 'Optimization (Mathematical Theory)'

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Fukasawa, Ricardo. "Single-row mixed-integer programs : theory and computations /." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24660.

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Thesis (Ph.D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.
Committee Chair: William J. Cook; Committee Member: Ellis Johnson; Committee Member: George Nemhauser; Committee Member: Robin Thomas; Committee Member: Zonghao Gu

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Luo, Min. "Perturbation analysis and optimization of fork-join queueing networks." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/14901.

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Hearnes, Warren E. II. "Near-optimal intelligent control for continuous set-point regulator problems via approximate dynamic programming." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/24882.

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Wong, Man-kwun, and 黃文冠. "Some sensitivity results for time-delay optimal control problems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31223655.

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Elhedhli, Samir. "Interior-point decomposition methods for integer programming : theory and application." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37887.

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Mixed integer programming (MIP) provides an important modeling and decision support tool for a wide variety of real-life problems. Unfortunately, practical MIPs are large-scale in size and pose serious difficulties to the available solution methodology and software.
This thesis presents a novel solution approach for large-scale mixed integer programming that integrates three bodies of research: interior point methods, decomposition techniques and branch-and-bound approaches. The combination of decomposition concepts and branch-and-bound is commonly known as branch-and-price, while the integration of decomposition concepts and interior point methods lead to the analytic centre cutting plane method (ACCPM). Unfortunately, the use of interior point methods within branch-and-bound methods could not compete with simplex based branch-and-bound due to the inability of "warm" starting.
The motivation for this study stems from the success of branch-and-price and ACCPM in solving integer and non-differentiable optimization problems respectively and the quest for a method that efficiently integrates interior-point methods and branch-and-bound.
The proposed approach is called an Interior Point Branch-and-Price method (IP-B&P) and works as follows. First, a problem's structure is exploited using Lagrangean relaxation. Second, the resulting master problem is solved using ACCPM. Finally, the overall approach is incorporated within a branch-and-bound scheme. The resulting method is more than the combination of three different techniques. It addresses and fixes complications that arise as a result of this integration. This includes the restarting of the interior-point methods, the branching rule and the exploitation of past information as a warm start.
In the first part of the thesis, we give the details of the interior-point branch-and-price method. We start by providing, discussing and implementing new ideas within ACCPM, then detail the IP-B&P method and its different components. To show the practical applicability of IP-B&P, we use the method as a basis for a new solution methodology for the production-distribution system design (PDSD) problem in supply chain management. In this second part of the thesis, we describe a two-level Lagrangean relaxation heuristic for the PDSD. The numerical results show the superiority of the method in providing the optimal solution for most of the problems attempted.

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Lam, Yun-sang Albert, and 林潤生. "Theory of optimization and a novel chemical reaction-inspired metaheuristic." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B4322412X.

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Lam, Yun-sang Albert. "Theory of optimization and a novel chemical reaction-inspired metaheuristic." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B4322412X.

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Li, Xinxin. "Some operator splitting methods for convex optimization." HKBU Institutional Repository, 2014. https://repository.hkbu.edu.hk/etd_oa/43.

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Many applications arising in various areas can be well modeled as convex optimization models with separable objective functions and linear coupling constraints. Such areas include signal processing, image processing, statistical learning, wireless networks, etc. If these well-structured convex models are treated as generic models and their separable structures are ignored in algorithmic design, then it is hard to eﬀectively exploit the favorable properties that the objective functions possibly have. Therefore, some operator splitting methods have regained much attention from diﬀerent areas for solving convex optimization models with separable structures in diﬀerent contexts. In this thesis, some new operator splitting methods are proposed for convex optimiza- tion models with separable structures. We ﬁrst propose combining the alternating direction method of multiplier with the logarithmic-quadratic proximal regulariza- tion for a separable monotone variational inequality with positive orthant constraints and propose a new operator splitting method. Then, we propose a proximal version of the strictly contractive Peaceman-Rachford splitting method, which was recently proposed for the convex minimization model with linear constraints and an objective function in form of the sum of two functions without coupled variables. After that, an operator splitting method suitable for parallel computation is proposed for a convex model whose objective function is the sum of three functions. For the new algorithms, we establish their convergence and estimate their convergence rates measured by the iteration complexity. We also apply the new algorithms to solve some applications arising in the image processing area; and report some preliminary numerical results. Last, we will discuss a particular video processing application and propose a series of new models for background extraction in diﬀerent scenarios; to which some of the new methods are applicable. Keywords: Convex optimization, Operator splitting method, Alternating direction method of multipliers, Peaceman-Rachford splitting method, Image processing

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Achmatowicz, Richard L. (Richard Leon). "Optimal control problems on an infinite time horizon." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66052.

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李澤康 and Chak-hong Lee. "Nonlinear time-delay optimal control problem: optimality conditions and duality." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1995. http://hub.hku.hk/bib/B31212475.

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Lee, Chak-hong. "Nonlinear time-delay optimal control problem : optimality conditions and duality /." [Hong Kong] : University of Hong Kong, 1995. http://sunzi.lib.hku.hk/hkuto/record.jsp?B16391640.

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Law, S. L. "Financial optimization problems." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.426391.

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The major objective of this thesis is to study optimization problems in finance. Most of the effort is directed towards studying the impact of transaction costs in those problems. In addition, we study dynamic meanvariance asset allocation problems. Stochastic HJB equations, Pontryagin Maximum Principle and perturbation analysis are the major mathematical techniques used. In Chapter 1, we introduce the background literature. Following that, we use the Pontryagin Maximum Principle to tackle the problem of dynamic mean-variance asset allocation and rediscover the doubling strategy. In Chapter 2, we present one of the major results of this thesis. In this chapter, we study a financial optimization problem based on a market model without transaction costs first. Then we study the equivalent problem based on a market model with transaction costs. We find that there is a relationship between these two solutions. Using this relationship, we can obtain the solution of one when we have the solution of another. In Chapter 3, we generalize the results of chapter 2. In Chapter 4, we use Pontryagin Maximum Principle to study the problem limit of the no-transaction region when transaction costs tend to 0. We find that the limit is the no-transaction cost solution.

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韓祖淵 and Cho-yuen Han. "A unified game theory approach to H-infinity control and filtering." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31235815.

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Han, Cho-yuen. "A unified game theory approach to H-infinity control and filtering /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18635520.

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Heymann, Benjamin. "Mathematical contributions for the optimization and regulation of electricity production." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX052/document.

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Nous présentons notre contribution sur la régulation et l’optimisation de la production d’électricité.La première partie concerne l’optimisation de la gestion d’un micro réseau. Nous formulons le programme de gestion comme un problème de commande optimal en temps continu, puis nous résolvons ce problème par programmation dynamique à l’aide d’un solveur développé dans ce but : BocopHJB. Nous montrons que ce type de formulation peut s’étendre à une modélisation stochastique. Nous terminons cette partie par l’algorithme de poids adaptatifs, qui permet une gestion de la batterie du micro réseau intégrant le vieillissement de celle-ci. L’algorithme exploite la structure à deux échelles de temps du problème de commande.La seconde partie concerne des modèles de marchés en réseaux, et en particulier ceux de l’électricité. Nous introduisons un mécanisme d’incitation permettant de diminuer le pouvoir de marché des producteurs d’énergie, au profit du consommateur. Nous étudions quelques propriétés mathématiques des problèmes d’optimisation rencontrés par les agents du marché (producteurs et régulateur). Le dernier chapitre étudie l’existence et l’unicité des équilibres de Nash en stratégies pures d’une classe de jeux Bayésiens à laquelle certains modèles de marchés en réseaux se rattachent. Pour certains cas simples, un algorithme de calcul d’équilibre est proposé.Une annexe rassemble une documentation sur le solveur numérique BocopHJB
We present our contribution on the optimization and regulation of electricity produc- tion.The first part deals with a microgrid Energy Management System (EMS). We formulate the EMS program as a continuous time optimal control problem and then solve this problem by dynamic programming using BocopHJB, a solver developed for this application. We show that an extension of this formulation to a stochastic setting is possible. The last section of this part introduces the adaptative weights dynamic programming algorithm, an algorithm for optimization problems with different time scales. We use the algorithm to integrate the battery aging in the EMS.The second part is dedicated to network markets, and in particular wholesale electricity markets. We introduce a mechanism to deal with the market power exercised by electricity producers, and thus increase the consumer welfare. Then we study some mathematical properties of the agents’ optimization problems (producers and system operator). In the last chapter, we present some pure Nash equilibrium existence and uniqueness results for a class of Bayesian games to which some networks markets belong. In addition we introduce an algorithm to compute the equilibrium for some specific cases.We provide some additional information on BocopHJB (the numerical solver developed and used in the first part of the thesis) in the appendix

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Hartline, Jason D. "Optimization in the private value model : competitive analysis applied to auction design /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/7015.

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Voisei, Mircea Dan. "First-order necessary optimality conditions for nonlinar optimal control problems." Ohio : Ohio University, 2004. http://www.ohiolink.edu/etd/view.cgi?ohiou1091111473.

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Roda, Fabio. "Integrating high-level requirements in optimization problems : theory and applications." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/pastel-00817782.

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Nous utilisons, ensemble, l'Ingénierie Système et la Programmation mathématique pour intégrer les exigences de haut niveau dans des problèmes d'optimisation. Nous appliquons cette méthode à trois types différents de système. (1) Les Systèmes d'Information (SI), c. à. D. Les réseaux des ressources, matérielles, logicielles et utilisateurs, utilisés dans une entreprise, doivent fournir la base des projets qui sont lancés pour répondre aux besoins commerciaux/des affaires (business). Les SI doivent être capables d'évoluer au fil des remplacements d'une technologie par une autre. Nous proposons un modèle opérationnel et une formulation de programmation mathématique qui formalise un problème de priorisation qui se présente dans le contexte de l'évolution technologique d'un système d'information. (2) Les Recommender Systems (RS) sont un type de moteur de recherche dont l'objectif est de fournir des recommandations personnalisées. Nous considérons le problème du design des Recommender Systems dans le but de fournir de bonnes, intéressantes et précises suggestions. Le transport des matériaux dangereux entraine plusieurs problèmes liés aux conséquences écologiques des incidents possibles. (3) Le système de transport doit assurer le transport, pour l'élimination en sécurité des déchets dangereux, d'une façon telle que le risque des possibles incidents soit distribué d'une manière équitable parmi la population. Nous considérons et intégrons dans des formulations de programmation mathématique deux idées différentes d'équité
We mix Mathematical Programming (MP) and Systems Engineering (SE) modelling methods and integrate system-level requirements in optimization problems. We use MP, in the first phases of the design process, as a common methodology to model prototypes that fulfil high-level requirements, consistently with the holistic, top-down approach of SE. This approach is applied to three different kinds of system. (1)Information systems, i. E. The network of communication channels, hardware, software and trained people used within an enterprise to help planning and control, are required to provide a basis for numerous IT projects that are launched in order to respond to the needs of the business. The information system shall ensure profitable services and it shall be maintainable and extensible. We propose an operational model and a mathematical programming formulation expressing a generic global prioritization problem occurring in the context of a technological evolution of an information system. (2)Recommender systems (RS) are a kind of search engine and aim to provide personalized recommendations. We consider the problem of designing recommender systems in order to provide good, interesting and accurate suggestions. (3)The transportation of hazardous materials (hazmat) entails several issues due to the environmental consequences of possible accidents. The transportation system shall ensure safe disposal of hazardous waste in such a way that the risk of potential catastrophic accident is equitably distributed over the population. We consider and integrate in MP formulations two different ideas of equity

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Ali, Shirook M. Nikolova Natalia K. "Efficient sensitivity analysis and optimization with full-wave EM solvers." *McMaster only, 2004.

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Lewis, Mark. "Bias optimality in a two-class nonstationary queueing system." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/24378.

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譚熙嘉 and Hei-Ka Patrick Tam. "Optimization approaches to robust pole assignment in control system design." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B3123933X.

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Xu, Li, and 徐力. "Some combinatorial optimization problems related to network encoding complexity." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/197559.

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Network coding is a novel technique to improve the throughput of networks to transfer messages from sources to sinks. Before the birth of network coding, intermediate nodes can only forward the received messages. In a network coding scheme, the intermediate nodes are allowed to mix the received messages from different incoming links. Network coding has found a wide range of applications, such as peer-to-peer networks, distributed storage and content distribution. The theory of network encoding complexity aims to deal with the question what the minimum number of encoding nodes needed in networks is. In order to tackle this question, we convert it into a combinatorial optimization problem. For directed networks, I examine the number of “mergings”, a special type of graph structure. Consider an acyclic directed network G with l source-sink pairs. Let ci denote the minimum size of edge-cut between i-th source-sink pair for 1 ≤ i ≤ l. Then, by Menger’s theorem, there exists a group of ci edge-disjoint paths (Menger’s paths) between i-th source-sink pair. Although within the same group these paths are edge-disjoint, the paths from different groups may have to merge with each other. It is known that by choosing Menger’s paths appropriately, the number of mergings among different groups of Menger’s paths is always bounded by a constant, which is independent of the size of G. The tightest such constant for the all the above-mentioned networks is denoted byM(c1, c2, . . . , cl) when all sources are distinct, and by M∗(c1, c2, . . . , cl) when all sources are identical. It turns out that M and M∗ are closely related to the network encoding complexity for a variety of networks, such as multicast networks, two-way networks and networks with multiple sessions of unicast. Computation of these two important functions, however, appears to be rather difficult; so far there are no explicit formulas for M and M∗ for a generic parameter c1, c2, . . . , cl. In this thesis, I derive exact values of and tighter bounds on M and M∗ for some parameters, and establish the inequality relationships between M and M∗. For undirected networks, I examine the number of “hubs”, the vertices of degree at least three. Compared to directed networks, study on network en-coding complexity in undirected networks has seen little progress. Consider an undirected network G with l source-sink pairs. For i = 1, 2, . . . , l, let ci de-note the minimum size of vertex-cut between i-th source-sink pair. I study H (c1, c2, . . . , cl), the minimum number of hubs needed in an undirected network with min-cut constraints. The function H is closely related to network en-coding complexity for undirected networks. I prove that under some constraints, regardless of the size of the undirected networks, such minimum number is always bounded above and I derive tight upper bounds for some special parameters. In particular, for two pairs of sources and sinks, I present a novel path-searching algorithm, the analysis of which is instrumental for the derivations of the tight upper bounds.
published_or_final_version
Mathematics
Doctoral
Doctor of Philosophy

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Lou, Jian. "Study on efficient sparse and low-rank optimization and its applications." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/543.

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Sparse and low-rank models have been becoming fundamental machine learning tools and have wide applications in areas including computer vision, data mining, bioinformatics and so on. It is of vital importance, yet of great difficulty, to develop efficient optimization algorithms for solving these models, especially under practical design considerations of computational, communicational and privacy restrictions for ever-growing larger scale problems. This thesis proposes a set of new algorithms to improve the efficiency of the sparse and low-rank models optimization. First, facing a large number of data samples during training of empirical risk minimization (ERM) with structured sparse regularization, the gradient computation part of the optimization can be computationally expensive and becomes the bottleneck. Therefore, I propose two gradient efficient optimization algorithms to reduce the total or per-iteration computational cost of the gradient evaluation step, which are new variants of the widely used generalized conditional gradient (GCG) method and incremental proximal gradient (PG) method, correspondingly. In detail, I propose a novel algorithm under GCG framework that requires optimal count of gradient evaluations as proximal gradient. I also propose a refined variant for a type of gauge regularized problem, where approximation techniques are allowed to further accelerate linear subproblem computation. Moreover, under the incremental proximal gradient framework, I propose to approximate the composite penalty by its proximal average under incremental gradient framework, so that a trade-off is made between precision and efficiency. Theoretical analysis and empirical studies show the efficiency of the proposed methods. Furthermore, the large data dimension (e.g. the large frame size of high-resolution image and video data) can lead to high per-iteration computational complexity, thus results into poor-scalability of the optimization algorithm from practical perspective. In particular, in spectral k-support norm regularized robust low-rank matrix and tensor optimization, traditional proximal map based alternating direction method of multipliers (ADMM) requires to evaluate a super-linear complexity subproblem in each iteration. I propose a set of per-iteration computational efficient alternatives to reduce the cost to linear and nearly linear with respect to the input data dimension for matrix and tensor case, correspondingly. The proposed algorithms consider the dual objective of the original problem that can take advantage of the more computational efficient linear oracle of the spectral k-support norm to be evaluated. Further, by studying the sub-gradient of the loss of the dual objective, a line-search strategy is adopted in the algorithm to enable it to adapt to the Holder smoothness. The overall convergence rate is also provided. Experiments on various computer vision and image processing applications demonstrate the superior prediction performance and computation efficiency of the proposed algorithm. In addition, since machine learning datasets often contain sensitive individual information, privacy-preserving becomes more and more important during sparse optimization. I provide two differentially private optimization algorithms under two common large-scale machine learning computing contexts, i.e., distributed and streaming optimization, correspondingly. For the distributed setting, I develop a new algorithm with 1) guaranteed strict differential privacy requirement, 2) nearly optimal utility and 3) reduced uplink communication complexity, for a nearly unexplored context with features partitioned among different parties under privacy restriction. For the streaming setting, I propose to improve the utility of the private algorithm by trading the privacy of distant input instances, under the differential privacy restriction. I show that the proposed method can either solve the private approximation function by a projected gradient update for projection-friendly constraints, or by a conditional gradient step for linear oracle-friendly constraint, both of which improve the regret bound to match the nonprivate optimal counterpart.

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Huang, Hui. "Optimal control of piecewise continuous stochastic processes." Bonn : [s.n.], 1989. http://catalog.hathitrust.org/api/volumes/oclc/23831217.html.

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Shin, Dong-Ryeol. "Optimal control of a finite state markov process under counting observation and applications to integrated networks." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/13081.

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Ko, Sung-Seok. "Behavior of fork-join networks, and effect of variability in service systems." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/24376.

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Cheng, Tak Sum. "Stochastic optimal control in randomly-branching environments." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/713.

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Shim, Sangho. "Large scale group network optimization." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31737.

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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Ellis L. Johnson; Committee Member: Brady Hunsaker; Committee Member: George Nemhauser; Committee Member: Jozef Siran; Committee Member: Shabbir Ahmed; Committee Member: William Cook. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Zhao, Kun. "Mathematical Methods for Network Analysis, Proteomics and Disease Prevention." Digital Archive @ GSU, 2012. http://digitalarchive.gsu.edu/math_diss/6.

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This dissertation aims at analyzing complex problems arising in the context of dynamical networks, proteomics, and disease prevention. First, a new graph-based method for proving global stability of synchronization in directed dynamical networks is developed. This method utilizes stability and graph theories to clarify the interplay between individual oscillator dynamics and network topology. Secondly, a graph-theoretical algorithm is proposed to predict Ca2+-binding site in proteins. The new algorithm enables us to identify previously-unknown Ca2+-binding sites, and deepens our understanding towards disease-related Ca2+-binding proteins at a molecular level. Finally, an optimization model and algorithm to solve a disease prevention problem are described at the population level. The new resource allocation model is designed to assist clinical managers to make decisions on identifying at-risk population groups, as well as selecting a screening and treatment strategy for chlamydia and gonorrhea patients under a fixed budget. The resource allocation model and algorithm can have a significant impact on real treatment strategy issues.

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Mackenzie, Neil C. "The independent quadratic optimisation algorithm for the active control of noise and vibration /." Title page, contents and abstract only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09phm15742.pdf.

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Wang, Chen. "Regulation and optimization methodology for smart grid in Chinese electric grid operators using quality function deployment, equilibrium theory, fractal theory and mathematical programming." Thesis, Brunel University, 2014. http://bura.brunel.ac.uk/handle/2438/11123.

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As the world is increasingly dependent on energy for the economic and social development and China’s Total Net Electricity Generation （TNEG） has remained the highest since 1996 due to its rapid economic growth, it is important to closely examine the operations of China’s electric power market, particularly the State Grid Corporation of China (SGCC) since it is the largest Electric Power Grid Operator (EPGO) in both China and the world. This research has addressed the problem and the urgent needs for the development of a sound framework and methodology for the effective regulation and optimization of the operations and quality management of the SGCC. Based on the critical literature review, the aspects and steps of the solution to the problem have been progressively presented. Firstly, a Country Wealth (CW) curve has been developed to characterize electricity generation in terms of TNEG, with China’s unique position identified. Further, the data has clearly indicated that China’s TNEG has also been closely correlated with the economic growth and the carbon emissions during the 30 years period of 1980-2010. Secondly, compared with the Equilibrium Energy Regulation Model, there are clear deficiencies and problems with the current regulation of China’s electric power market. The improvements in the integration of regulation strategies and the formation of one single effective regulator have been identified and proposed. Thirdly, a uniform regulation structure and framework based on fractal theory and QFD (quality function deployment) has been developed to integrate the existing and future electric power strategies, including smart grid strategy and sustainable development strategy(etc.). Through the use of QFD, the EPGO (SGCC) functions and operations can be prioritized and appropriately designed. Finally, the QFD methodology has been extended to achieve the optimization of quality and service operations given the target cost of the business processes. The methodology can be applied to both business and technical processes of the EPGOs since quality may be interpreted as a total quality involving the needs and expectations of various customers or stakeholders.

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Bless, Robert R. "Time-domain finite elements in optimal control with application to launch-vehicle guidance." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/20211.

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Kelome, Djivèdé Armel. "Viscosity solutions of second order equations in a separable Hilbert space and applications to stochastic optimal control." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/29159.

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Zhang, Jiapu. "Derivative-free hybrid methods in global optimization and their applications." Thesis, University of Ballarat, 2005. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/34054.

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In recent years large-scale global optimization (GO) problems have drawn considerable attention. These problems have many applications, in particular in data mining and biochemistry. Numerical methods for GO are often very time consuming and could not be applied for high-dimensional non-convex and / or non-smooth optimization problems. The thesis explores reasons why we need to develop and study new algorithms for solving large-scale GO problems .... The thesis presents several derivative-free hybrid methods for large scale GO problems. These methods do not guarantee the calculation of a global solution; however, results of numerical experiments presented in this thesis demonstrate that they, as a rule, calculate a solution which is a global one or close to it. Their applications to data mining problems and the protein folding problem are demonstrated.
Doctor of Philosophy

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Hutchison, Matthew Gerry. "Multidisciplinary optimization of high-speed civil transport configurations using variable-complexity modeling." Diss., This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06062008-165715/.

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Tendero, Yohann. "Mathematical theory of the Flutter Shutter : its paradoxes and their solution." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00752409.

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This thesis provides theoretical and practical solutions to two problems raised by digital photography of moving scenes, and infrared photography. Until recently photographing moving objects could only be done using short exposure times. Yet, two recent groundbreaking works have proposed two new designs of camera allowing arbitrary exposure times. The flutter shutter of Agrawal et al. creates an invertible motion blur by using a clever shutter technique to interrupt the photon flux during the exposure time according to a well chosen binary sequence. The motion-invariant photography of Levin et al. gets the same result by accelerating the camera at a constant rate. Both methods follow computational photography as a new paradigm. The conception of cameras is rethought to include sophisticated digital processing. This thesis proposes a method for evaluating the image quality of these new cameras. The leitmotiv of the analysis is the SNR (signal to noise ratio) of the image after deconvolution. It gives the efficiency of these new camera design in terms of image quality. The theory provides explicit formulas for the SNR. It raises two paradoxes of these cameras, and resolves them. It provides the underlying motion model of each flutter shutter, including patented ones. A shorter second part addresses the the main quality problem in infrared video imaging, the non-uniformity. This perturbation is a time-dependent noise caused by the infrared sensor, structured in columns. The conclusion of this work is that it is not only possible but also efficient and robust to perform the correction on a single image. This permits to ensure the absence of ''ghost artifacts'', a classic of the literature on the subject, coming from inadequate processing relative to the acquisition model.

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Kumar, Manish. "Converting some global optimization problems to mixed integer linear problems using piecewise linear approximations." Diss., Rolla, Mo. : University of Missouri-Rolla, 2007. http://scholarsmine.umr.edu/thesis/pdf/Kumar_09007dcc803c8e68.pdf.

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Thesis (M.S.)--University of Missouri--Rolla, 2007.
Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed December 7, 2007) Includes bibliographical references (p. 28).

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Kediyal, Prashant C. "Comparison of possible optimization methods for design of optical filters /." Electronic thesis, 2004. http://etd.wfu.edu/theses/available/etd-05022004-113931/.

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Li, Zhijin. "Task-based optimization of 3D breast x-ray imaging using mathematical observers." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLN038.

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La mammographie, une modalité 2D d'imagerie du sein par rayons X, a montré son efficacité pour réduire la mortalité par cancer du sein. Aujourd'hui, la tomosynthèse numérique du sein, une modalité 3D d'imagerie du sein par rayons X, prend une place de plus en plus importante dans la pratique clinique, et est reconnue de plus en plus souvent comme ayant le potentiel de remplacer la mammographie dans un proche avenir. Pour évaluer plusieurs aspects de la tomosynthèse, des études cliniques sont nécessaires. Mais les études cliniques sont coûteuses et présentent des risques supplémentaires pour les patientes dus à l'utilisation de radiations ionisantes. Les études cliniques virtuelles ont pour objectif d'offrir une approche alternative en utilisant des simulations numériques. Dans cette thèse, nous nous intéressons à plusieurs éléments intervenants dans une telle étude clinique virtuelle. Dans un premier temps, nous analysons l'état de l'art sur la caractérisation analytique des champs aléatoires 3D pour la simulation de la texture du sein par rayons X. Nous nous intéressons aussi à l'estimation de caractéristiques statistiques des images du sein par rayons X (densité, indice spectral). Puis nous développons un nouveau modèle de texture 3D du sein basé sur la géométrie stochastique, et qui permet de simuler des images 2D et 3D réalistes du sein. Nous considérons le problème de l'inférence d'un tel modèle à partir d'une base d'images cliniques 3D. Ensuite, nous développons un observateur mathématique basé sur la théorie textit{a contrario} de la perception visuelle, pour modéliser la détection des microcalcifications par des radiologues dans des images 2D et 3D du sein. Tous ces composants sont utilisés pour implémenter une étude clinique entièrement numérique. La pertinence des résultats obtenus montre l'utilité de ces études cliniques virtuelles et nous incite à en développer de plus élaborées dans le futur
Full field digital mammography, a 2D x-ray breast imaging modality has been proved to reduce the breast cancer mortality. Today, digital breast tomosynthesis, a 3D x-ray breast imaging modality, is being integrated in clinical practice and is believed to replace standard mammography in the near future. To assess the clinical performance of various aspects of tomosynthesis, clinical trials are needed. Clinical trials are burdensome, expensive and may impose increased risk to the patient due to additional radiation exposure. Virtual Clinical Trials aim to offer a more efficient alternative by using computational components. Today, active research is ongoing to develop computational components dedicated to 2D and 3D breast imaging, especially to 3D tomosynthesis. This thesis aims to advance several aspects in the development of Virtual Clinical Trials. First, we focused on analytical characterization of state-of-the-art 3D random field breast texture models. The estimation of statistical characteristics (breast density, spectral index) from clinical x-ray breast images was also studied. Next, we proposed a mathematically traceable 3D breast texture model based on stochastic geometry, that allows to simulate realistic 2D and 3D images. The statistical inference of the texture model parameters from a database of clinical 3D breast images was also tackled. We then developed a mathematical observer based on the textit{a contrario} theory, that allows to model the microcalcification detection process by radiologists in 2D and 3D breast images. Finally, these two proposed components were applied to implement a virtual clinical trial experiment, demonstrating their potential in the conduct of more advanced virtual clinical studies in the future

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Ranga, Mithun Kumar. "Fixed order optimal control using genetic algorithms /." free to MU campus, to others for purchase, 2004. http://wwwlib.umi.com/cr/mo/fullcit?p1426097.

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Pascual, Francisco L. "Essays on the optimal selection of series functions." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2007. http://wwwlib.umi.com/cr/ucsd/fullcit?p3274811.

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Thesis (Ph. D.)--University of California, San Diego, 2007.
Title from first page of PDF file (viewed October 4, 2007). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references.

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Mason, Richard. "A chordal sparsity approach to scalable linear and nonlinear systems analysis." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:c4a978aa-185e-4029-a887-6aa2ab9efb37.

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In this thesis we investigate how the properties of chordal graphs can be used to exploit sparsity in several optimisation problems that arise in control theory. In particular, we focus on analysis and synthesis problems that involve semidefinite constraints and can be formulated as semidefinite programming (SDP) problems. Using a relationship between chordal graphs and sparse semidefinite matrices, we decompose the semidefinite constraints in the associated SDP problems into multiple, smaller semidefinite constraints along with some additional equality constraints. The benefit of this approach is that for sparse dynamical systems we can solve significantly larger analysis and synthesis problems than is possible using traditional dense methods. We begin by considering the properties of chordal graphs and their connection to sparse positive semidefinite matrices. We then turn our attention to the problem of constructing Lyapunov functions for linear time-invariant (LTI) systems. From this starting point, we derive methods of exploiting chordal sparsity in other analysis problems found in control theory. In particular, this approach is applied to the problem of bounding the input-output properties of systems via the KYP lemma for both continuous and discrete-time systems. We then consider how the properties of chordal graphs can be exploited in the SDPs that arise in static state feedback controller synthesis problems for LTI systems. We show that the sparse inverse property of the maximum determinant completion of a partial positive matrix can be used to design controllers with a pre-specified sparsity pattern. We then consider how to exploit chordal sparsity when designing a static state feedback controller to minimise the H-infinity norm of an LTI system. Next we shift from linear systems to nonlinear systems and develop a chordal sparsity approach to scalable stability analysis of systems with polynomial dynamics using the Sums of Squares (SOS) technique. We develop a method of exploiting chordal sparsity that avoids the computationally costly step of forming the coefficient matrix in the SOS problem. We then apply this method to the problem of constructing Lyapunov functions for systems with correlatively sparse polynomial vector fields. Finally, we conclude by discussing some directions for future research.

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Hjort, Mattias. "Bestämning av optimal fordonspark -Distribution av bitumen vid Nynäs AB." Thesis, Linköping University, Department of Mathematics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2903.

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Nynas produces bitumen at two refineries in Sweden. The bitumen is shipped to seven depots along the swedish coast line, and from the depots special trucks handle the transportation to customers. Recently Nynas has transformed its supply chain and closed down a few depots. At the moment the company is considering a further reduction of the number of depots. In connection to these discussions an analyse of the companys distributionsystem and of possible changes is required. In this thesis an optimization model is developed that simulates Nynas distribution of bitumen from the depots to the customers. The model is used to investigate the required vehicle fleet size for a number of different scenarios, that is with different depots closed down. The question to be answered is, thus, what depots could be closed without any dramatic increase in the required vehicle fleet size? Scenarios where customers are allocated an increased storage capacity are also studied.

The distribution model that is developed is an inventory route planning problem. It is solved by column generation. Each column represents a route and is generated by a subproblem with restrictions on permitted working hours for the truck drivers. Integer solutions are generated heuristically.

Simulations that have been performed with the model reveals interesting differences concerning how the distribution is handled in different parts of Sweden. In western Sweden the transportation planning works well, but the distribution in the central parts of the country could be planned in a better way. Results from simulations also show that the depots in Norrköping and Västerås could be closed down without increasing the vehicle fleet. Probably, the existing vehicle fleet size will be sufficient even with the Kalmar-depot closed down. Nevertheless, Nynas transportation suppliers will have to purchase new vehicles if the Sandarne-depot is to be closed.

Another interesting conclusion that can be drawn from this thesis is that there is a potential for reducing the vehicle fleet size if the storage capacity is increased at a few chosen customers. A considerably small increase in the storage capacity at a few big customers that are located far from the depots will have a great effect.

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Axelsson, Henrik. "Optimal Control of Switched Autonomous Systems: Theory, Algorithms, and Robotic Applications." Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-04052006-131248/.

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Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2006.
Ashraf Saad, Committee Member ; Spyros Reveliotis, Committee Member ; Anthony Yezzi, Committee Member ; Erik Verriest, Committee Member ; Yorai Wardi, Committee Co-Chair ; Magnus Egerstedt, Committee Chair.

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Cramm, Kenneth Peter. "Solutions to the Chinese Postman Problem." CSUSB ScholarWorks, 2000. https://scholarworks.lib.csusb.edu/etd-project/1683.

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Considering the Chinese Postman Problem, in which a mailman must deliver mail to houses in a neighborhood. The mailman must cover each side of the street that has houses, at least once. The focus of this paper is our attempt to discover the optimal path, or the least number of times each street is walked. The integration of algorithms from graph theory and operations research form the method used to explain solutions to the Chinese Postman Problem.

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Sochor, Jana, and Cecilia Yu. "A Heuristic Method for Routing Snowplows After Snowfall." Thesis, Linköping University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2550.

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Sweden experiences heavy snowfall during the winter season and cost effective road maintenance is significantly affected by the routing of snowplows. The routing problem becomes more complex as the SwedishNational Road Administration (Vägverket) sets operational requirements such as satisfying a time window for each road segment.

This thesis focuses on route optimization for snowplows after snowfall; to develop and implement an algorithm for finding combinations of generated routes which minimize the total cost. The results are compared to those stated in the licentiate thesis by Doctoral student Nima Golbaharan (2001).

The algorithm calculates a lower bound to the problem using a Lagrangian master problem. A common subgradient approach is used to find near-optimal dual variables to be sent to a column-generation program which returns routes for the snowplows. A greedy heuristic chooses a feasible solution, which gives an upper bound to the problem. This entire process is repeated as needed.

This method for routing snowplows produces favorable results with a relatively small number of routes and are comparable to Golbaharan's results. An interesting observation involves the allocation of vehicles in which certain depots were regularly over- or under-utilized. This suggests that the quantity and/or distribution of available vehicles may not be optimal.

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Werner, Adrian. "Bilevel stochastic programming problems: Analysis and application to telecommunications." Doctoral thesis, Norwegian University of Science and Technology, Faculty of Social Sciences and Technology Management, 2005. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-577.

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We analyse several facets of bilevel decision problems under uncertainty. These problems can be interpreted as an extension of stochastic programming problems where part of the uncertainty is attributed to the behaviour of another actor.

The field of decision making under uncertainty with bilevel features is quite new and most approaches focus on the interactions and relations between the decision makers. In contrast to these studies, the approach of bilevel stochastic programming pursued here stresses the stochastic programming aspect of the problem formulation. The framework enables a direct application of stochastic programming concepts and solution methods to the bilevel relationship between the actors. Thus more complex problem structures can be studied and the aspect of uncertainty can be treated adequately.

Our analysis covers both theoretical and more practically oriented issues. We study different formulations of one and two stage bilevel stochastic programming problems and state necessary optimality conditions for each of the problem instances. Additionally we present a solution algorithm utilising a stochastic quasi-gradient method. A further study is concerned with the uniqueness of the minima of a convex stochastic programming problem with uncertainty about the decision variables. We state conditions on the distribution of the parameters representing the uncertainty such that the minima of the optimisation problem are unique. We formulate a model of competition and collaboration of two different types of telecom service providers, the owner of a bottleneck facility and a virtual network operator. This represents an application of a bilevel stochastic programming formulation to a liberalised telecommunications environment. Furthermore, the utilisation of the bilevel stochastic programming framework and the developed solution concepts for the analysis of principal agent models is demonstrated. Also here the background of a regulated telecom environment, more specific the relations between a regulator and a regulated telecommunications company, was chosen.

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Goel, Gagan. "Algorithms for budgeted auctions and multi-agent covering problems." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29679.

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Thesis (Ph.D)--Computing, Georgia Institute of Technology, 2010.
Committee Chair: Vazirani, Vijay; Committee Member: Kalai, Adam; Committee Member: Mihail, Milena; Committee Member: Tetali, Prasad; Committee Member: Thomas, Robin. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Mehta, Aranyak. "Algorithmic Game Theory." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7220.

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The interaction of theoretical computer science with game theory and economics has resulted in the emergence of two very interesting research directions. First, it has provided a new model for algorithm design, which is to optimize in the presence of strategic behavior. Second, it has prompted us to consider the computational aspects of various solution concepts from game theory, economics and auction design which have traditionally been considered mainly in a non-constructive manner. In this thesis we present progress along both these directions. We first consider optimization problems that arise in the design of combinatorial auctions. We provide an online algorithm in the important case of budget-bounded utilities. This model is motivated by the recent development of the business of online auctions of search engine advertisements. Our algorithm achieves a factor of $1-1/e$, via a new linear programming based technique to determine optimal tradeoffs between bids and budgets. We also provide lower bounds in terms of hardness of approximation in more general submodular settings, via a PCP-based reduction. Second, we consider truth-revelation in auctions, and provide an equivalence theorem between two notions of strategy-proofness in randomized auctions of digital goods. Last, we consider the problem of computing an approximate Nash equilibrium in multi-player general-sum games, for which we provide the first subexponential time algorithm.

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Junique, Stéphane. "Surface-normal multiple quantum well electroabsorption modulators based on GaAs-related materials." Licentiate thesis, KTH, Microelectronics and Information Technology, IMIT, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-292.

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Dissertations / Theses on the topic 'Optimization (Mathematical Theory)'

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