Probabilistic choice models are used by economists, psychologists, and marketing scientists in the analysis of choice behavior involving discrete, or quantal choice alternatives. The most widely-used of these is the multinomial logit model, which is a special case of the Luce model. These models are appealing for their simplicity and elegance, but have some severe flaws which have motivated continued research on more complex choice models. This has given rise to a need for efficient numerical algorithms for parameter estimation. One of the most important estimators is the maximum likelihood estimator, which historically has been avoided due to its computational difficulty. New algorithms for maximum likelihood estimation of choice models are developed which exploit the special structure inherent in the problem. The approach taken is to write the problem as a generalized regression problem; this gives rise to two formulations in which the Hessian is written as the sum of two matrices. The first is readily available from information already calculated for the gradient, and the second is expensive to calculate. The algorithms approximate the second piece by means of a least-change secant update, and solve the problem using a model/trust region approach involving model switching. Both approaches are successful, with one approach dominating the other in test examples using the multinomial logit, elimination-by-aspects, and Batsell-Polking models. Additional work includes a comparison of estimators in which it is demonstrated that the maximum likelihood and nonlinear least squares estimators have small-sample properties which are superior to other estimators proposed in the literature, especially those utilizing generalized least squares.

Many current algorithms for nonlinear constrained optimization problems determine a search direction by solving a quadratic programming subproblem. The global convergence properties are addressed by using a line search technique and a merit function to modify the length of the step obtained from the quadratic program. In unconstrained optimization, trust region strategies have been very successful. In this thesis we present a new approach for equality constrained optimization problems based on a trust region strategy. The direction selected is not necessarily the solution of the standard quadratic programming subproblem.

Multi-objective optimization problems are characterized by the need to consider multiple, and possibly conflicting, objectives in the solution process. We present an approach based on the use of interactive computer graphics to obtain qualitative information from a user about approximate solutions. We then use this qualitative information to transform the multi-objective optimization problem into a single-objective optimization problem that we may solve using standard techniques. Preliminary convergence results for the Nelder-Mead simplex algorithm are presented. Techniques for updating the single-objective problem after each piece of information is obtained from the user are described. These techniques are based on the duality theory for linear and quadratic programming. A software system for the subclass of 1-dimensional curve-fitting problems is also described.

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Interior-point methods have not only shown their efficiency for linear and some nonlinear programming problems, but also for cutting plane methods and large scale optimization. The analytic center cutting plane method uses the analytic center of the current polyhedral approximation of the feasible region to add a new cutting plane. In this thesis, analytic center cutting plane and path-following interior-point methodologies are used to solve the following problems: (1) convex feasibility problems defined by a deep cut separation oracle; (2) convex optimization problems involving a nonlinear objective and a constraint set defined implicitly by a separation oracle; (3) variational inequalities involving a nonlinear operator and a convex set explicitly defined; (4) variational inequalities involving an affine operator and a constraint set defined implicitly by a deep cut separation oracle; and (5) variational inequalities involving a nonlinear operator and a constraint set defined implicitly by a deep cut separation oracle. Here, the oracle is a routine that takes as input a test point. If the point belongs to the feasible region, it answers "yes", otherwise it answers "no" and returns a cut separating the point from the feasible region. Complexity bounds are established for algorithms developed for Cases 1, 2 and 4. The algorithm developed for Case 3 will be proven to be convergent, whereas, in Case 5, the developed algorithm will be shown to find an approximate solution in finite time.

Although attention has been given to parental attitudes regarding enrollment of their high-risk infants in research, there is a paucity of knowledge in the literature, which investigates nurses’ experiences of caring for high-risk infants involved in research. Consequently, there is little understanding of how caring for these infants impacts nursing care. The purpose of this research was to arrive at an increased understanding of neonatal nurses' experiences in caring for high-risk infants involved in research. Attention was given to exploring neonatal intensive care unit (NICU) nurses’ perspectives towards neonatal research and the notion of risk to involving high-risk infants in research, their perceived roles and responsibilities with regards to high-risk infants in research, and the impact of research on caring for high-risk infants. This study was built on the research program of the student’s supervisor that seeks to increase the knowledge base of the nature of risk in child health research. An exploratory descriptive study within the qualitative paradigm was used. Seven semi-structured interviews, one focus group interview, and field notes were used to obtain information from seven NICU nurses. All of the qualitative data that emerged was analyzed using the constant comparative data analysis technique. Data analysis revealed that safeguarding their patients, or being a “safety net”, was the essence of nurses’ experiences of caring for high-risk infants involved in research. The nurses described their main role was the provision of a safe environment, regardless of the infants’ involvement in research. Acting as a “safety net” involved the nurses always being on guard and knowledgeable about their patients’ care. The following three themes further depicting the safeguarding experience emerged: feelings within, keeping it near and dear, and making it safer. The first theme, feelings within, uncovered nurses’ mixed emotions when caring for infants involved in research, which ranged from positive feelings to feelings of moral distress. The second theme, keeping it near and dear, referred to the uncomfortable feelings and memories that nurses held about situations in which they felt infants enrolled in research had suffered because of their inability of not being able to fully safeguard them. Some of the nurses expressed regretting their choices, such as not speaking up on a patient’s behalf, while others described it as a learning process, which eventually contributed to their abilities to safeguard infants. The third theme, making it safer, was based on the nurses’ enthusiasm about the future of neonatal research. The nurses identified many ways in which child health researchers, bedside nurses, REB members, and parents could minimize the risks of involving high-risk infants in research. This study yielded new insights about how NICU nurses care for high-risk infants involved in research that may be used to improve the protection of high-risk infants in research and ultimately contribute to the quality of care for these infants. Recommendations for nursing practice, education, and research are suggested.

Whereas the literature on English as a Second Language (ESL) instruction has flourished over the last thirty years, very little in the literature addresses issues concerning research with participants who are non-native speakers of English (NNSE). For this qualitative study, six researchers affiliated with a western prairie university were interviewed and asked to reflect on what ethics means to them, which ethical issues are of greatest importance to them when working with NNSE participants, and the role of research ethics boards (REBs). Issues of language, culture and power were found to be key themes as was a deep respect on the part of the researchers towards their participants. In addition, REBs were found to be lacking and in need of reconsideration. These findings suggest that there exists a distinction between institutional ethics (ethics as it pertains to REBs) and individual ethics (ethics as envisioned by researchers).

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