Operations research combines the applications of optimization, probability and statistics to solve problems in different domains including business, energy and utilities, health services, financial services and logistics. In order to solve today’s complex system environment, operations research often works at the intersection of these disciplines, such as the use of optimization in the estimation of large scale statistical models, optimal collection of information, and stochastic optimization.
Systems engineers know how to develop and use mathematical and statistical models to help solve these decision problems. Like other engineers, they are problem formulators and solvers. Their work requires the formation of a mathematical model of a system and the analysis and prediction of the consequences of alternate modes of operating the system.
Best System Identification Using Ordinal Optimization
D. Ahn Given a number of stochastic systems and a finite sampling budget, we consider an ordinal optimizationproblem to find an optimal allocation that maximizes the likelihood of selecting the system with the bestperformance. Generalized linear models...
Distributionally Robust Discrete Optimization
Z. Y. Long We study the discrete optimization problem under the distributionally robust framework. We optimize theEntropic Value-at-Risk, which is a coherent risk measure and is also known as Bernstein approximation for the chance constraint. We propose...
Fast Algorithms for Big Data Analytics
A. M.-C. So The ubiquity of big datasets and the desire to extract information and knowledge from them have motivated the development of a wide array of data analytics tools in recent years. Many of these tools aim at identifying the most informative...
Fast Algorithms for Distributionally Robust Optimization
A. M.-C. So
Distributionally robust optimization (DRO) has received much attention lately due to its ability to incorporate data uncertainty in and provide robustness interpretation of optimization models. Many of the DRO problems that arise in practice...
Financial Systemic Risk
N Chen Financial institutions knit a complex network. They interconnect with each other directly through active borrowing-and-lending activities and holding significant amount of marketable securities against each other. In normal times, this network...
Langevin Dynamics for Sampling and Global Optimization
X.F. Gao Langevin Dynamics (LD) have received considerable attention recently in the field of machine learning and computational statistics. LD has been proven to be powerful techniques for two closely-related tasks: 1) globally optimizing a non-convex...
Multi-Attribute Utility Preference Robust Optimization and Robust Spectral Risk Optimization
H. Xu Decision maker’s preference in utility or risk determines which utility function or risk measure to use in an optimal decision making problem.
Ambiguity arises when there is incomplete information about decision maker’s preference and suc...
Nonconvex Optimization and Global Optimization
D. Li and C. K. Ng
The research goal is to develop equivalent transformations for generating a saddle point for nonconvex optimization problems. A saddle point condition is a sufficient condition for optimality. A saddle point can be generated in...
Nonconvex Optimization for Big Data Analysis: Theory and Practice
A. M.-C. So Optimization is now widely reckoned as an indispensable tool in big data analysis. Although convex optimization remains a powerful, and is by far the most extensively used, paradigm for tackling big data applications, we have witnessed a...
Nonlinear Integer Programming
D. Li and C. K. Ng
The research goal is to establish convergent duality theory and to develop efficient solution algorithms for large-scale nonlinear integer programming problems. The fundamental target underlying our theoretical development is to...
Risk in Project Selection
Z. Y Long We consider a project selection problem where each project has an uncertain return with partially characterized probability distribution. The decision maker selects a feasible subset of projects so that the risk of the portfolio return not...
Robust Mechanism for Risk Management in Absence of Complete Information on Risk Preference
H. Xu Quantitative measure of risk is a key element in risk management for many financial institutions and regulatory authorities.Over the past few decades, many risk measures have been introduced. In all of these research, it is assumed that the information...
Statistical Robustness of Stochastic Generalized Equations
H. Xu
Stochastic generalized equations (SGE) provide a unified framework for characterizing the first order optimality and equilibrium conditions of many decision making problems with random data.
The current research of SGE focuses on asymptotic...
Stochastic and Dynamical Optimization Techniques forMachine Learning
H.-T. Wai The recent success of machine learning is inseparable from the advancements of stochastic optimizationtechniques. We look at two different directions in this research. The first one deals with `big-data’ spread across a network of machines. W...
Target-based Dynamic Decision Making
Z. Y. Long
We investigate a dynamic decision model that facilitates a target-oriented decision maker in regulating her risky consumption based on her desired target consumption level in every period in a finite planning horizon. We focus on dynamic...