This dissertation presents novel advancements in the field of continuous nonlinear optimization, focusing on the development of efficient second-order methods for second-order conic programs (SOCPs) and continuous nonlinear two-stage optimization problems. The primary focus is on the theory and computations of Sequential Quadratic Programming (SQP) methods, which are widely used...
Multistage optimization is a prominent modeling tool to solve a broad range of dynamic decision-making problems in the presence of uncertainty. However, computing optimal policies is intractable, since they are obtained by considering all possible realizations of uncertainties and subsequent future decisions over time. To overcome these challenges, we present...
Optimization via simulation (OvS) is the practice of minimizing or maximizing the expected value of the output of a stochastic simulation model with respect to controllable decision variables. Stochastic simulation is a standard tool within operations research and is often required to model complex systems subject to uncertainty where it...
In this dissertation, we study models and methods to address uncertainties that can vary in optimization problems. Robust optimization is a popular approach for optimization under uncertainty, especially if limited information is available about the distribution of the uncertainty. It models the uncertainty through sets and finds a robust optimal...
The goal of this thesis is to design practical algorithms for nonlinear optimization in the case where the objective function is deterministic or stochastic. Problems of this nature arise in many applications including machine learning and image processing. The thesis is divided into four main chapters. Chapters \ref{chap:Inexact}, \ref{chap:Adasample} and...
Cancer radiation therapy relies on optimized treatment plans whose quality assessment is judged by dosimetric planning aims. It is computationally prohibitive to incorporate the planning aims into the optimization models. Therefore, there exists a disconnect between the two steps of (1) optimizing a plan and (2) evaluating the optimized plan,...
The vast majority of interactions between customers and service providers are experiences that extend over time. Service systems that deliver excellent customer experience achieve greater customer satisfaction and therefore customer loyalty, and eventually raise revenue. The temporal aspects of service delivery have not yet been analyzed as carefully as its...