Dissertations / Theses on the topic 'Trust Region Model'

Modern nonlinear programming solvers can efficiently handle very large scale optimization problems when accurate derivative information is available. However, black box or derivative free modeling components are often unavoidable in practice when the modeled phenomena may cross length and time scales. This work is motivated by examples in chemical process optimization where most unit operations have well-known equation oriented representations, but some portion of the model (e.g. a complex reactor model) may only be available with an external function call. The concept of a surrogate model is frequently used to solve this type of problem. A surrogate model is an equation oriented approximation of the black box that allows traditional derivative based optimization to be applied directly. However, optimization tends to exploit approximation errors in the surrogate model leading to inaccurate solutions and repeated rebuilding of the surrogate model. Even if the surrogate model is perfectly accurate at the solution, this only guarantees that the original problem is feasible. Since optimality conditions require gradient information, a higher degree of accuracy is required. In this work, we consider the general problem of hybrid glass box/black box optimization, or gray box optimization, with focus on guaranteeing that a surrogate-based optimization strategy converges to optimal points of the original detailed model. We first propose an algorithm that combines ideas from SQP filter methods and derivative free trust region methods to solve this class of problems. The black box portion of the model is replaced by a sequence of surrogate models (i.e. surrogate models) in trust region subproblems. By carefully managing surrogate model construction, the algorithm is guaranteed to converge to true optimal solutions. Then, we discuss how this algorithm can be modified for effective application to practical problems. Performance is demonstrated on a test set of benchmarks as well as a set of case studies relating to chemical process optimization. In particular, application to the oxycombustion carbon capture power generation process leads to significant efficiency improvements. Finally, extensions of surrogate-based optimization to other contexts is explored through a case study with physical properties.

In this thesis a numerical study of the one dimensional viscous Burgers equation is conducted. The discretization techniques Finite Differences, Finite Element Method and Group Finite Elements are applied and their impact on model reduction techniques, namely Proper Orthogonal Decomposition (POD), Group POD and the Discrete Empirical Interpolation Method (DEIM), is studied. This study is facilitated by examination of several common ODE solvers. Embedded in this process, some results on the structure of the POD basis and an alternative algorithm to compute the POD subspace are presented. Various numerical studies are conducted to compare the different methods and the to study the interaction of the spatial discretization on the ROM through the basis functions. Moreover, the results are used to investigate the impact of Reduced Order Models (ROM) on Optimal Control Problems. To this end, the ROM is embedded in a Trust Region Framework and the convergence results of Arian et al. (2000) is extended to POD-DEIM. Based on the convergence theorem and the results of the numerical studies, the emphasis is on implementation strategies for numerical speedup.
Master of Science

This study focused on how local politicians in Kalmar perceive journalists and their intertwined relationship. We based our study on the theoretical understanding of today’s media-centric democratic society. The ‘adversary model’ offered an understanding of the intricate relations between politicians and journalists. The relationship builds on constant trade where both parties are dependent on each other. Politicians exchange information to gain attention in the media. Journalists needs politicians as important sources of information and have the power to control the exposure that politicians get in the public eye. This study was researched and conducted through qualitative interviews with local politicians.

We found that experienced politicians have developed an understanding for journalistic work and that it is important to have a good relationship to reach out to their constituency. This professional relationship has to be kept at arm’s length as it otherwise risks to become too muddled. We learned that politicians are well aware of the need to adapt to media conditions – there were, however, examples of breakdowns in this precarious relationship.

The politicians in our study delivered several examples of how media adaptation is managed, e g how press conferences are scheduled according to media deadlines and are held at suitable locations so that photographers can get good pictures. Trust appeared to be the crucial condition for a rewarding relationship. Every politician in our study agreed that it is all a question of trust.

For parameter inversion problems governed by systems of partial differential equations, such as those arising in Diffuse Optical Tomography (DOT), even the cost of repeated objective function evaluation can be overwhelming. Despite the linear (in the state variable) nature of the DOT problem, the nonlinear parameter inversion process is dominated by the computational burden of solving a large linear system for each source and frequency. To compute the Jacobian for use in Newton-type methods, an adjoint solve is required for each detector and frequency. When a three-dimensional tomography problem may have nearly 1,000 sources and detectors, the computational cost of an optimization routine is a large burden. While techniques from model order reduction can partially alleviate the computational cost, obtaining error bounds in parameter space is typically not feasible. In this work, we examine two different remedies based on stochastic estimates of the objective function. In the first manuscript, we focus on maximizing the efficiency of using stochastic estimates by replacing our objective function with a surrogate objective function computed from a reduced order model (ROM). We use as few as a single sample to detect a misfit between the full-order and surrogate objective functions. Once a sufficiently large difference is detected, it is necessary to update the ROM to reduce the error. We propose a new technique for improving the ROM with very few large linear solutions. Using this techniques, we observe a reduction of up to 98% in the number of large linear solutions for a three-dimensional tomography problem. In the second manuscript, we focus on establishing a robust algorithm. We propose a new trust region framework that replaces the objective function evaluations with stochastic estimates of the improvement factor and the misfit between the model and objective function gradients. If these estimates satisfy a fixed multiplicative error bound with a high, but fixed, probability, we show that this framework converges almost surely to a stationary point of the objective function. We derive suitable bounds for the DOT problem and present results illustrating the robust nature of these estimates with only 10 samples per iteration.
Doctor of Philosophy
For problems such as medical imaging, the process of reconstructing the state of a system from measurement data can be very expensive to compute. The ever increasing need for high accuracy requires very large models to be used. Reducing the computational burden by replacing the model with a specially constructed smaller model is an established and effective technique. However, it can be difficult to determine how well the smaller model matches the original model. In this thesis, we examine two techniques for estimating the quality of a smaller model based on randomized combinations of sources and detectors. The first technique focuses on reducing the computational cost as much as possible. With the equivalent of a single randomized source, we show that this estimate is an effective measure of the model quality. Coupled with a new technique for improving the smaller model, we demonstrate a highly efficient and robust method. The second technique prioritizes robustness in its algorithm. The algorithm uses these randomized combinations to estimate how the observations change for different system states. If these estimates are accurate with a high probability, we show that this leads to a method that always finds a minimum misfit between predicted values and the observed data.

Thesis (M. S.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2008.
Committee Chair: Anton Kleywegt; Committee Co-Chair: Alexander Shapiro; Committee Member: Charles Rosa; Committee Member: Shabbir Ahmed; Committee Member: Sigrun Andradottir.

Diese Dissertation umfasst drei Aufsätzen, die sich mit Erwartungen, Entscheidungen und deren Rückwirkung auf die Umgebung beschäftigen. Der erste Aufsatz untersucht die Binnenwanderung von Ost- nach Westdeutschland. Dabei wird der Zusammenhang von Variation in ökonomischen Disparitäten zwischen der Ursprungs- und der Zielregion und Bildungsniveau, Alter und Arbeitsmarktstatus der wandernden Bevölkerung untersucht. Mit Hilfe der SOEP Daten von 1993 bis 2011 gelangt die Untersuchung zu dem Ergebnis, dass regionale Disparitäten in Verbindung mit der Selbstselektion der Wandernden stehen. Während die Wandernden im Durchschnitt jünger und besser ausgebildet als die Bleibenden sind, verringert sich dieser Unterschied, wenn die Differentiale in den Arbeitslosenquoten zwischen den Regionen steigen. Im zweiten Aufsatz entwickle ich ein Modell zur Untersuchung von prosozialem Verhalten in Begegnungen mit Fremden. Durch das Abstrahieren von Möglichkeiten der Reputationsbildung oder des Bestraftwerdens, entfallen die wesentlichen strategischen Motive für prosoziales Verhalten. Die Entscheidung prosozial zu Handeln ist dann nicht mehr strategisch vorteilhaft sondern intrinsisch motiviert durch Altruismus und einer Neigung sich an das Verhalten anderer anzupassen. In einem zweiten Schritt untersuche ich, ob die Erkenntnisse des Modells mit dem empirisch beobachteten Verhalten übereinstimmen. Der dritte Aufsatz skizziert eine (mögliche) Verhaltensstruktur und notwendige Bedingungen auf Mikroebene, die zu den beobachteten Verhaltensunterschieden in prosozialem Verhalten zwischen dem ländlichen und städtischen Raum führen. Den Rahmen des hier entwickelten Modells bildet das bekannte Gefangenen Dilemma, das wiederholt mit zufällig zugeordneten Partnern einer großen Gesellschaft gespielt wird. Das Modell bezieht Merkmale ein, die sich häufig in realen Begegnungen wiederfinden: imperfekte Information, freiwillige Teilnahme und eine Neigung sich dem Verhalten anderer anzupassen.
This thesis consists of three essays that analyze choices and beliefs to explore how both lead to adaptive behavior. The first essay examines the positive net migration flow from the eastern to western parts of Germany. The migration decision is substantially based on expectations about future developments. With economic conditions changing substantially over the past 20 years in the eastern part of Germany, the incentives to migrate have also altered, so changing the composition of the east-to-west migrant body. This essay explores variations in economic disparities between the region of origin and region of destination, relating them to changes in the skill level, age and labor force status of the migrant population. Analyzing SOEP data from 1993-2011, the findings suggest that, with falling wage differentials, older migrants are less frequent job-to-job movers and are more likely to be non-working prior to migration. Furthermore, while migrants tend to be younger and better educated than stayers, the group of movers becomes partly less distinct from the group of stayers with respect to the skill and age composition when regional disparities in employment opportunities increase. The second and the third essay of this thesis model the decision making process in social interactions between strangers. In these situations, choices are often affected by beliefs about others behavior. In the second essay of this work, I develop a simple model of prosocial behavior for encounters between strangers. By abstracting from the possibility of reputation building and punishment between anonymous partners, I remove the main strategic motives for prosocial behavior so reducing it to a simple non-strategic decision. The principal motivation to behave prosocially is then intrinsic, based on altruism, with a taste for conforming to the behavior of others. In this way, individual decisions are conditional on the behavior of others. Emerging equilibria will then explain the occurrence of prosocial or cooperative behavior within a given society. In a second step, I analyze whether the model’s predictions are consistent with the empirical evidence on the link between beliefs and prosocial behavior using data on blood donations. The third essay outline a (possible) micro-structure and conditions which lead to the observed urban-rural differences in cooperative behavior using agent-based modeling. The model presented here adapts the familiar framework of a prisoners dilemma which is played repeatedly with randomly matched members of a large population. I introduce features that are often found in real world interactions: imperfect information, voluntary participation and a taste for conforming to majority behavior. In this analysis, peoples beliefs about the level of cooperation in the population and their resulting behavior are determined endogenously. Both are governed principally by the experience that they derive from interactions. I present results of an agentbased simulation in order to study the emerging dynamic relationships, to examine how cooperative behavior evolves over time under different circumstances, and to determine how urban-rural differences in behavior emerge. The factors that give rise to rural-urban differences are heterogeneity in individual loss aversion or risk taking, and limited migration possibilities between rural and urban areas.

The increasing interest in the real estate investment has led to the emergence of new real estate investment vehicles, adding more complexity to the real estate market which increasingly resembles to financial markets. Academic research regarding real estate market, from a financial perspective, has been developed, essentially, considering modern finanance theories. Nevertheless, a new trend of thought named behavioural finance that assume the market inefficiency as well as the irrationality of market, and develope models based on individuals' behaviour. This doctoral thesis applies behavioural finance theories into the analysis and investment in the real estate market, showing that behavioural models improve the results of their actors' decision making. On the one hand, it has been developed an econometric model of the prices of new housing in Spain, implying not only an extrinsic and intrinsic combined approach, but also hipothesis inherited from the Behavioral School in order to explain and predict the Spanish real estate market and understand the periods of irrational exhuberance. On the other hand, it has been analysed from a financial perspective, the market performance of the first SOCIMI (Spanish Real Estate Investment Trusts) established in Spain, developing a model that allows to predict the price-to-net-asset-value (P/NAV) ratio of a SOCIMI. In addition, it is proved that the constitution of a SOCIMI is an efficient alternative for real estate companies to obtain liquidity from their assets, compared to other alternatives such as assets' disposal or obtaining bank finance.
El aumento del interés inversor en el sector inmobiliario, el cual forma parte tanto de carteras de pequeños inversores hasta grandes fondos de inversión internacionales, ha llevado a la aparición de nuevos vehículos de inversión inmobiliaria dotando al mercado de mayor complejidad, asemejándolo cada vez más a los mercados financieros. La investigación académica entorno al mercado inmobiliario, desde una perspectiva financiera, ha tomado como referencia las finanzas modernas surgidas de la escuela económica neoclásica y basadas en la teorías de carteras de Markowitz, del mercado de capitales de Sharpe y del mercado eficiente de Fama. No obstante, una nueva corriente denominada finanzas conductuales, desarrolladas a partir de las teorías de la escuela conductual, han puesto en duda los modelos de las finanzas modernas debido al dudoso encaje de sus modelos en el mercado inmobiliario, así como en la escasa previsión de la crisis de los mercados financieros del año 2008. Así, la falta de un mercado único de comercialización, la ineficiencia informacional, la heterogeneidad e iliquidez de los activos, son algunas de las características del sector inmobiliario que no se adaptan a las hipótesis de la teoría económica moderna, y que, por tanto, exigen un nuevo planteamiento que parece resolverse mediante las finanzas conductuales. La escuela conductual asume la ineficiencia de los mercados y la irracionalidad de sus actores (los cuales influyen en los precios infravalorándolos o sobrevalorándolos de forma persistente y duradera) y desarrolla modelos en base al comportamiento real de las personas. La presente tesis doctoral aplica las finanzas conductuales para el análisis e inversión en el mercado inmobiliario evidenciando que los modelos conductuales comportan una mejora en las tomas de decisiones de sus actores. Por un lado, se ha desarrollado un modelo econométrico del precio de la vivienda nueva en España que supone no sólo un acercamiento que combina el enfoque extrínseco e intrínseco, si no que incorpora también hipótesis de la escuela conductual a fin de explicar y prever el ciclo inmobiliario español y comprender los períodos de exuberancia irracional. Adicionalmente, se ha procedido a analizar desde una perspectiva financiera, el comportamiento de las primeras SOCIMI (Sociedades Anónimas Cotizadas de Inversión en el Mercado Inmobiliario) constituidas en España, desarrollando un modelo que prevé el valor del ratio P/NAV, obtenido como el cociente entre la cotización (P) y el valor neto de los activos (NAV) de una SOCIMI. Así mismo se comprueba que la constitución de una SOCIMI es una alternativa eficiente para las sociedades inmobiliarias para la obtención de liquidez de sus activos, frente a otras alternativas como la enajenación directa de éstos o la obtención de financiación bancaria. Finalmente, aunque la liquidez de las primeras SOCIMI constituidas en España es moderada, se evidencia que son un vehículo de inversión inmobiliaria competitivo en términos de rentabilidad y riesgo, previéndose una mejora en el medio plazo a medida se constituyan SOCIMI de mayor tamaño y se disponga de series históricas de rentabilidades más amplias.

The method of quasilinearization for the solution of nonlinear two point boundary value problems is Newton's method for a nonlinear differential operator equation. Semilocal convergence results, with the attendant error estimates, are available from the Kantorovich Theorem. Since the linear boundary value problem to be solved at each iteration must be discretized, it is natural to consider quasilinearization in the framework of Inexact Newton methods. Conditions on the size of the relative residual of the linear differential equation, given by an approximate solution, can then be specified to guarantee rapid local convergence. If initial value techniques are used to solve the linear boundary value problem then it is possible to implement an integration step selection scheme so that the residual criteria is satisfied by the approximate solution. The result is a sequence of approximate solutions to the linear boundary value problems that converge to the true solution of the nonlinear boundary value problem. A model trust region approach to globalization can be extended to this infinite dimensional problem to allow convergence from an arbitrary initial point. The double dogleg implementation yields a globally convergent algorithm that is robust in solving difficult problems.

The goal of this work was to develop metamodels of the MDO framework piMDO and provide new research in metamodeling strategies. The theory of existing metamodels is presented and implementation details are given. A new trust region scheme --- metamodel trust region optimization (MTRO) --- was developed. This method uses a progressive level of minimum validity in order to reduce the number of sample points required for the optimization process. Higher levels of validity require denser point distributions, but the reducing size of the region during the optimization process mitigates an increase the number of points required. New metamodeling strategies include: inherited optimal latin hypercube sampling, hybrid latin hypercube sampling, and kriging with BFGS. MTRO performs better than traditional trust region methods for single discipline problems and is competitive against other MDO architectures when used with a CSSO algorithm. Advanced metamodeling methods proved to be inefficient in trust region methods.

A recent approach for the construction of nonlinear optimization software has been to allow an algorithm to choose between two possible models to the objective function at each iteration. The model switching algorithm NL2SOL of Dennis, Gay and Welsch and the hybrid algorithms of Al-Baali and Fletcher has proven highly effective in practice. Although not explicitly formulated as multi-model methods, many other algorithms implicitly perform a model switch under certain circumstances (e.g., resetting a secant model to the exact value of the Hessian). We present a trust region formulation for multi-model methods which allows the efficient incorporation of an arbitrary number of models. Global convergence can be shown for three classes of algorithms under different assumptions on the models. First, essentially any multi-model algorithm is globally convergent if each of the models is sufficiently well behaved. Second, algorithms based on the central feature of the NL2SOL switching system are globally convergent if one model is well behaved and each other model obeys a "sufficient predicted decrease" condition. No requirement is made that these alternate models be quadratic. Third, algorithms of the second type which directly enforce the "sufficient predicted decrease" condition are globally convergent if a single model is sufficiently well behaved.

碩士
國立暨南國際大學
資訊工程學系
94
Three-dimensional data acquisition techniques form the basis of reverse engineering. In order to obtain the complete information of an object surface, it is usually required to scan the object from different angles of views. Therefore, the data sets have to be registered to compute the coordinate transformation matrices among them. However, the registration results may contain estimation errors owing to the incorrect correspondences and measurement noise. The effect of registration error may be not obvious in pair-wise registration, but the accumulated registration error often results in serious flaws in global registration. Therefore, global registration is one of the key issues in reverse engineering. Because the amount of data and variables that have to be dealt with in global registration can be very large, reducing the global registration error is a difficult task. A feasible approach is to linearize Rodrigues’ formula for rotation matrices so that the constrained large scale nonlinear optimization problem can be simplified to be tractable. However, when the accumulation error is too large to be linearized, the linearization solutions will fail. In this thesis, we propose a trust-region algorithm that can automatically adjust the trust radius of linearization zone so that we can take advantages of both the efficiency of linearization and the accuracy of nonlinear constraints. Experiments showed that the proposed method is efficient and accurate.

Parmi les méthodes d’estimation de paramètres de loi de probabilité en statistique, le maximum de vraisemblance est une des techniques les plus populaires, comme, sous des conditions l´egères, les estimateurs ainsi produits sont consistants et asymptotiquement efficaces. Les problèmes de maximum de vraisemblance peuvent être traités comme des problèmes de programmation non linéaires, éventuellement non convexe, pour lesquels deux grandes classes de méthodes de résolution sont les techniques de région de confiance et les méthodes de recherche linéaire. En outre, il est possible d’exploiter la structure de ces problèmes pour tenter d’accélerer la convergence de ces méthodes, sous certaines hypothèses. Dans ce travail, nous revisitons certaines approches classiques ou récemment d´eveloppées en optimisation non linéaire, dans le contexte particulier de l’estimation de maximum de vraisemblance. Nous développons également de nouveaux algorithmes pour résoudre ce problème, reconsidérant différentes techniques d’approximation de hessiens, et proposons de nouvelles méthodes de calcul de pas, en particulier dans le cadre des algorithmes de recherche linéaire. Il s’agit notamment d’algorithmes nous permettant de changer d’approximation de hessien et d’adapter la longueur du pas dans une direction de recherche fixée. Finalement, nous évaluons l’efficacité numérique des méthodes proposées dans le cadre de l’estimation de modèles de choix discrets, en particulier les modèles logit mélangés.
Maximum likelihood is one of the most popular techniques to estimate the parameters of some given distributions. Under slight conditions, the produced estimators are consistent and asymptotically efficient. Maximum likelihood problems can be handled as non-linear programming problems, possibly non convex, that can be solved for instance using line-search methods and trust-region algorithms. Moreover, under some conditions, it is possible to exploit the structures of such problems in order to speedup convergence. In this work, we consider various non-linear programming techniques, either standard or recently developed, within the maximum likelihood estimation perspective. We also propose new algorithms to solve this estimation problem, capitalizing on Hessian approximation techniques and developing new methods to compute steps, in particular in the context of line-search approaches. More specifically, we investigate methods that allow us switching between Hessian approximations and adapting the step length along the search direction. We finally assess the numerical efficiency of the proposed methods for the estimation of discrete choice models, more precisely mixed logit models.

A compatibility-based strut-and-tie model C-STM is proposed for analyzing deep beams and disturbed regions with particular emphasis on reinforced concrete bridge piers. In addition to the normal strut-and-tie force equilibrium requirements the model accounts for non-linear behavior through displacement compatibility using inelastic constitutive laws of cracked reinforced concrete. The model is implemented into widely used commercial structural analysis software and validated against results from previously conducted large scale experiments. A near full-scale experiment on a reinforced concrete sub-assemblage that represents cantilevered and straddle pier bents is conducted to investigate the shear-flexure performance of deep (disturbed) regions. Insights into the development of nonlinear behavior and the final collapse failure mechanism are then evaluated and accurately modeled using the C-STM. It is concluded that the proposed C-STM serves as an advanced method of analysis that can predict with suitable accuracy the force-deformation response of both D- and B- regions, deep beams, and beam-columns. This provides engineers with a supplementary analysis tool that can be used to assess the nonlinear behavior of bridge piers with stocky members and/or large disturbed regions.

Submitted in partial fulfilment of the requirements for the degree of Masters of Management in Finance and Investments In the Faculty of Commerce, Law and Management University of the Witwatersrand, Wits Business School, 2016
This paper presents a first time application of a variant of the concepts underpinning the Fed Model, amalgamated with the Bond-Stock Earnings Yield Differential, by applying it to the dividend yields of REIT indices. This modification is termed the yield gap, quantitatively constructed and adapted in this paper as the Reverse REIT-Bond Yield Gap. This metric is then used as the variable of interest in a multivariate Markov regime switching model framework, along with a set of three regressors. The REIT indices trailing dividend yield and associated metrics are the FTSE/EPRA NAREIT series. All data are from Bloomberg Terminals. This paper examines 11 markets, of which the EMEs are classified as Brazil, Mexico, Turkey and South Africa, whereas the advanced market counterparts are Australia, France, Japan, the Netherlands, Singapore, the United Kingdom, and the United States. The time-frame spans the period June 2013 until November 2015 for the EMEs, whilst their advanced market counterparts time-span covers the period November 2009 until November 2015. This paper encompasses a tri-fold research objective, and aims to accomplish them in a scientifically-based, objective and coherent fashion. Specifically, the purpose is in an attempt to gauge the reasons underlying EMEs observed anomalies entailing reverse REIT-Bond yield gaps, whereby their tenyear nominal government bonds out-yield their trailing dividend yields on their associated REIT indices; what drives fluctuations in this metric; and whether or not profitable tactical asset allocation strategies can be formulated to exploit any arbitrage mispricing opportunities. The Markov models were unable to generate clear-cut, definitive reasons regarding why EMEs experience this anomaly. Objectives two and three were achieved, except for France and Mexico. The third objective was also met. The REIT-Bond Yield Gaps static conditions have high probabilities of continuing in the same direction and magnitude into the future. In retrospection, the results suggest that by positioning an investment strategy, taking cognisance of the chain of economic events that are likely to occur following static REIT-Bond Yield Gaps, then investors, portfolio rebalancing and risk management techniques, hedging, targeted, tactical and strategic asset allocation strategies could be formulated to exploit any potential arbitrage profits. The REIT-Bond Yield Gaps are considered highly contentious, yet encompasses the potential for significant reward. The Fed Model insinuates that EME REIT markets are overvalued relative to their respective government bonds, whereas their advanced market counterparts exhibit the opposite phenomenon.
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