<p>The problem of finding a feasible solution to a system of linear inequalities arises in numerous contexts. In this dissertation, we consider solving a system of linear inequalities in view of unconstrained convex programming problems. Solution methods for solving systems with either finitely or infinitely many linear inequalities are proposed. Convergence properties and implementation issues are discussed. Some computational results are also included. <P>

<p>The primary objectives of this research are formulation and evaluation ofa Bayesian approach for selecting input models in discrete-eventstochastic simulation. This approach takes into account the model,parameter, and stochastic uncertainties that are inherent in mostsimulation experiments in order to yield valid predictive inferences aboutthe output quantities of interest. We use prior information to specify theprior plausibility of each candidate input model that adequately fits thedata, and to construct prior distributions on the parameters of eachmodel. We combine prior information with the likelihood function of thedata to compute the posterior model probabilities and the posteriorparameter distributions using Bayes' rule. This leads to a BayesianSimulation Replication Algorithm in which: (a) we estimate the parameteruncertainty by sampling from the posterior distribution of each model'sparameters on selected simulation runs; (b) we estimate the stochasticuncertainty by multiple independent replications of those selected runs;and (c) we estimate model uncertainty by weighting the results of (a) and(b) using the corresponding posterior model probabilities. We alsoconstruct a confidence interval on the posterior mean response from theoutput of the algorithm, and we develop a replication allocation procedurethat optimally allocates simulation runs to input models so as to minimizethe variance of the mean estimator subject to a budget constraint oncomputer time. To assess the performance of the algorithm, we propose someevaluation criteria that are reasonable within both the Bayesian andfrequentist paradigms. An experimental performance evaluation demonstratesthe advantages of the Bayesian approach versus conventional frequentisttechniques.<P>

<p>Successful e-commerce presupposes techniques by which autonomous trading entities can interoperate. Although much progress has been made on data exchange and payment protocols, interoperation in the face of autonomy is still inadequately understood. Current techniques, designed for closed environments, support only the simplest interactions.This dissertation concentrates on two themes. First, we develop a generic agent interaction model that supports agent coordination. We propose metacommitment patterns, which accommodate revisions and exceptions, to model agent interaction. We formalize metacommitment patterns declaratively in temporal logic. We apply statecharts to specify behavior models of agents who follow our commitment patterns. The statecharts provide an operational semantics, which can be used as a rigorous basis for agent coordination. We propose agent behavior models and prove that it operationally supports our temporal logic semantics. In this manner, we provide the basis for formally designing coordinated multiagent systems. Second, we apply agent behavior models for interoperation in e-commerce. This approach consists of (1) behavioral models to specify autonomous, heterogeneous agents representing different trading entities (businesses, consumers, brokers), (2) a metamodel that provides a language (based on XML) for specifying a variety of service agreements and accommodating exceptions and revisions, and (3) an execution architecture that supports persistent and dynamic (re)execution. Our implementation uses existing Java tool kits for parsing XML and building communicating agents. The main contributions of this dissertation are in developing some theoretical aspects of agent interaction with an emphasis on e-commerce.In addition, the proposed approach can also provide a rigorous basis for future standards for interoperation in e-commerce.<P>

<p> KARNOUB, RAZEK E. An Exact Bidirectional Approach to the Resource Constrained Project Scheduling Problem. (Under the direction of Salah E. Elmaghraby) The aim of this research is to develop a new approach to the Resource Constrained Project Scheduling Problem. Traditionally, most exact approaches to solve the problem have been either Integer Programming approaches or Branch and Bound (BaB) ones. Of the two, BaB procedures have proven to be the more successful computationally. But, while it is quite intuitive to conceive that the root node of a BaB search tree should be the start activity, it is no less conceivable that it be the terminal activity. Indeed, it is conceivable that the search starts from both ends and concludes somewhere in the middle of the ensuing trees. Unfortunately, BaB as a methodology is not amenable to deriving a termination criterion for such a procedure which guarantees optimality. To a large extent, this research can be seen as an attempt at accomplishing just that. We start with a comprehensive review of the literature related to the problem. We present a new Integer Programming model to describe it together with a `look-ahead' heuristic procedure which may be used along with it. The main advantage of this procedure is its ability to reflect planning over the short horizon in anticipation of changes to the project in the more future. Our chief contribution is in the third part of this study which sets up the problem as a Shortest Path Problem in two `state networks', forward and reverse, where the nodes reflect the precedence feasibility or partial completion of the activities of the project. We develop the conceptual tools to construct the networks and to properly detect a `path' between their sources from which a makespan optimal schedule could be derived. The theoretical constructs ultimately result in algorithms that solve the problem proceeding forward, in reverse, or bidirectionally. These algorithms have been tested on the J30 benchmark data set of Kolisch, Sprecher and Drexl (1995). Computational results show important advantages of the bidirectional approach but also point out significant avenues for improvement.<P>

<p>Many very large Markov chains can be modeled efficiently as Stochastic Automata Networks (SANs). A SAN iscomposed of individual automata that, for the most part, act independently, requiring only infrequentinteraction. SANs represent the generator matrix Q of the underlying Markov chain compactly as the sum ofKronecker products of smaller matrices. Thus, storage savings are immediate. The benefit of a SAN's compactrepresentation, known as the descriptor, is often outweighed by its tendency to make analysis of theunderlying Markov chain tough. Although iterative or projection methods have been used to solve the system P Q=0, the convergence to the stationary solution P is still unsatisfactory. SAN's compact representation hasmade the next logical research step of preconditioning thorny. Several preconditioners for SANs have beenproposed and tested, yet each has enjoyed little or no success. Encouraged by the recent success ofapproximate inverses as preconditioners, we have explored their potential as SAN preconditioners. Onepromising finding on approximate inverse preconditioner is the nearest Kronecker product (NKP) approximationintroduced by Pitsianis and Van Loan. In this dissertation, we approximate Q by the nearest Kronecker productfor a SAN with a Kronecker product, A1 D A2 D . . . D AN. Then, we take M= A1-1 A2-1 D . . . D AN-1 as ourSAN NKP preconditioner. We show how successful this NKP preconditioner is for SANs by testing it on severalexamples. We also introduce and catalogue some new results about the Kronecker product, an operation which isfundamental to this SAN research.<P>

Thesis (Ph.D.)--Lehigh University, 2009. / Adviser: David S. Wu.

Thesis (Ph.D.)--Lehigh University, 2009. / Adviser: Jeff Linderoth.

Thesis (M.S. in Operations Research)--Naval Postgraduate School, December 2009. / Thesis Advisor: Nussbaum, Daniel. Second Reader: Kang,Sung Jin. "December 2009." Description based on title screen as viewed on January 26, 2010. Author(s) subject terms: Defense acquisition, Korea Helicopter Program(KHP), Korea Utility Helicopter(KUH), Adaptive Cost Estimation Relationships(CERs). Includes bibliographical references (p. 31-33). Also available in print.

Thesis (Ph. D.)--University OF MICHIGAN.

Thesis (M.S. in Operations Research)--Naval Postgraduate School, June 2004. / Thesis advisor(s): Robert F. Dell. Includes bibliographical references (p. 41). Also available online.