Abstract

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.

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Management

Date of Award

January 2016

First Advisor

Mohit Tawarmalani

Committee Member 1

Jean-Philippe P Richard

Committee Member 2

Yanjun Li

Committee Member 3

Thanh Nguyen

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