Cardinality Constrained Optimization Problems

In this thesis, we examine optimization problems with a constraint that allows for only a certain number of variables to be nonzero. This constraint, which is called a cardinality constraint, has received considerable attention in a number of areas such as machine learning, statistics, computational finance, and operations management. Despite their practical needs, most optimization problems with a cardinality constraints are hard to solve due to their nonconvexity. We focus on constructing tight convex relaxations to such problems

Discordance Minimization-based Imputation Algorithms for Missing Values in Rating Data

Ratings are frequently used to evaluate and compare subjects in various applications, from education to healthcare, because ratings provide succinct yet credible measures for comparing subjects. However, when multiple rating lists are combined or considered together, subjects often have missing ratings, because most rating lists do not rate every subject in the combined list. In this study, we propose analyses on missing value patterns using six real-world data sets in various applications, as well as the conditions for applicability of imputation algorithms. Based on the special structures and properties derived from the analyses, we propose optimization models and algorithms that minimize the total rating discordance across rating providers to impute missing ratings in the combined rating lists, using only the known rating information. The total rating discordance is defined as the sum of the pairwise discordance metric, which can be written as a quadratic function. Computational experiments based on real-world and synthetic rating data sets show that the proposed methods outperform the state-of-the-art general imputation methods in the literature in terms of imputation accuracy.This preprint is cited as Park, Y.W., Kim, J., Zhu, D., Discordance Minimization-based Imputation Algorithms for Missing Values in Rating Data. arXiv, 2023; https://doi.org/10.48550/arXiv.2311.04035. Posted with permission. https://creativecommons.org/licenses/by/4.0

A Mathematical Programming Approach for Imputation of Unknown Journal Ratings in a Combined Journal Quality List

The quality of faculty scholarship and productivity is one of the primary measures for faculty evaluation in most academic institutions. Due to the diversity and interdisciplinary nature of modern academic research fields, it is increasingly important to use journal quality lists, with journal ratings, that offer credible measures of the worth of faculty scholarship. Despite the existence of such metrics, journal lists, by their very nature, exclude some well‐recognized journals. Consequently, academic institutions expend inordinate resources to assess the quality of unrated journals appropriately and equitably across disciplines. The current research proposes mathematical programming models as a path to determining unknown ratings of multiple journal quality lists, using only their known rating information. The objective of the models is to minimize the total number of instances where two journals are rated in opposite order by two different journal quality lists. Computational results based on journal quality list data in https://harzing.com/ indicate that the proposed methods outperform existing imputation algorithms with most realistic test data sets in terms of accuracy, root mean square error, and mean absolute deviation.This accept article is published as J. Kim, Y.W. Park*, and A.J. Williams (2019), “A Mathematical Programming Approach for Imputation of Unknown Journal Ratings in a Combined Journal Quality List,” Decision Sciences, 52(2);455-482. doi: 10.1111/deci.12400. Posted with permission</p