The United States (US) witnessed remarkable growth in annual long distance travel over the past few decades. Over half of the long distance travel in the US is made for pleasure, including visiting friends and relatives (VFR) and leisure activities. This trend could continue with increased use of information and communication technologies for socialization, and enhanced mobility being achieved using fuel-efficient (electric/hybrid) and technology enhanced vehicles. Despite these developments, and recent interest to implement alternate mass transit options to serve this market, not much exists on the measurement, analysis and modeling of long distance pleasure travel in the U.S. Statewide and national models are used to estimate long distance travel, but these are predominantly trip-based models, making it difficult to understand long distance trips as collection of household-level travel behavior. This form of travel behavior has been studied a lot in tourism, but in a piecemeal manner, such as to (from) a specific destination. Further, most of these studies are confined to analyzing leisure market, with VFR market gaining recognition only recently. In essence, annual household long distance pleasure travel behavior needs to be studied in a comprehensive manner rather than as isolated trips. This is because, most of these household travel decisions are undertaken considering their annual time and monetary budget, and their perceived cost to travel to one (or more) destination for given pleasure purpose on one (or more) occasion using a given mode of travel. Thus, the main objective of this dissertation is to develop a comprehensive behavioral model framework to analyze the above-discussed annual household long distance pleasure travel choices. To start the above effort, it is first required to collect detailed annual household travel data, last collected over two decades ago (e.g.: ATS, 1995). No such recent effort has been pursued due to the significant labor and economic resource required to undertake it. There exist recent surveys (NHTS, 2001), but collected over a shorter (four week) period, and require significant processing even to arrive at aggregate annual travel estimates. Second, besides surveys, there is a need for additional data to estimate households’ annual pleasure travel budget, and their cost to travel and stay at each of their potential destination choices, which are not readily available. Thus, as the first goal, this dissertation analyzes long distance travel reported across historical surveys (NPTS; ATS; NHTS), to understand the differences in their definition, enumeration of purpose and collection methods. The intent here is twofold, first to conceive a method to estimate annual travel from surveys with shorter collection period. Further, the second intent is to gather travel patterns from these historical datasets such that it informs the second goal of this dissertation, i.e. development of a behavioral framework to analyze annual household pleasure travel. To this effect, this research also analyzes pleasure expenditures using Consumer Expenditure Survey (CEX, BLS) data. Interestingly, the analysis reveals CEX pleasure travel expenditure pattern to be similar to the travel pattern reported for the same market segments in travel survey (ATS). Importantly, the above analysis informs the development of behavioral models, pursued as two distinct tasks to achieve the second goal. As the first task, a novel econometric model and forecasting procedure is developed to analyze a household’s annual long distance leisure travel decisions. Specifically, a households’ time spent across one (or more) destination and travel mode to such destination for leisure is modeled subject to time and money budget constraints. In this methodological framework, the destination choice is modeled as a continuous variable (time at destination) using Multiple-Discrete Continuous Extreme Value model (MDCEV). While, travel mode choice to these destination(s) are modeled as a discrete choice, through a nested Multinomial Logit Model (MNL), with price variation introduced across the above choice of destination(s) and travel modes (air/ground). This required estimating annual monetary budgets, travel cost and per night lodging cost for each sample household, with each of them having 210 potential destinations and 2 travel mode choices respectively. The second task, involved the development of a broader national model system to analyze households’ annual pleasure travel decisions such as: choice (duration) at destination(s), travel purpose (VFR or leisure), mode (airplane or auto) choice and trip frequencies to these destination(s) using the same dataset. It was modeled in two stages, with the first stage estimating households’ annual pleasure time budget using a stochastic frontier model. This budget was then used as constraint to analyze households’ annual choice of destination and purpose using a nested MDCEV-MNL model in the second stage. A log sum variable from a nested joint multinomial logit model of trip frequency and mode choice for each purpose (VFR or leisure) is also introduced as input at this stage. This model was then validated using a prediction procedure, and further applied to test a policy scenario (increase in travel cost). The above national pleasure travel demand model could be further enhanced by including monetary constraints and price variation as in the first task. Overall, the model system proposed in this dissertation forms the foundation for a national comprehensive long distance travel model. This could be achieved through inclusion of other prominent travel purpose such as business and commuting to the national travel demand model presented in this research.

This work is concerned with the construction of preconditioners for indefinite linear systems. The systems under investigation arise in the numerical solution of quadratic programming problems, for example in the form of Karush--Kuhn--Tucker (KKT) optimality conditions or in interior--point methods. Therefore, the system matrix is referred to as a KKT matrix. It is not the purpose of this thesis to investigate systems arising from general quadratic programming problems, but to study systems arising in linear quadratic control problems governed by partial differential equations. The KKT matrix is symmetric, nonsingular, and indefinite. For the solution of the linear systems generalizations of the conjugate gradient method, MINRES and SYMMLQ, are used. The performance of these iterative solution methods depends on the eigenvalue distribution of the matrix and of the cost of the multiplication of the system matrix with a vector. To increase the performance of these methods, one tries to transform the system to favorably change its eigenvalue distribution. This is called preconditioning and the nonsingular transformation matrices are called preconditioners. Since the overall performance of the iterative methods also depends on the cost of matrix--vector multiplications, the preconditioner has to be constructed so that it can be applied efficiently. The preconditioners designed in this thesis are positive definite and they maintain the symmetry of the system. For the construction of the preconditioners we strongly exploit the structure of the underlying system. The preconditioners are composed of preconditioners for the submatrices in the KKT system. Therefore, known efficient preconditioners can be readily adapted to this context. The derivation of the preconditioners is motivated by the properties of the KKT matrices arising in optimal control problems. An analysis of the preconditioners is given and various cases which are important for interior point methods are treated separately. The preconditioners are tested on a typical problem, a Neumann boundary control for an elliptic equation. In many important situations the preconditioners substantially reduce the number of iterations needed by the solvers. In some cases, it can even be shown that the number of iterations for the preconditioned system is independent of the refinement of the discretization of the partial differential equation. / Master of Science