CAREER: Computation, Theory, and Applications for Nonconvex Quadratic and Conic Optimization

University Of Iowa, Iowa City IA

Investigators

Abstract

ABSTRACT 0545514 Samuel Burer University of Iowa This project focuses on computation, theory, and applications in the field of optimization, a scientific discipline that plays an important role in the applied sciences, having a broad impact in numerous diverse areas of society, including defense, business, and health care. An important goal of the project is to communicate the relevance of optimization, and more generally, computer science and information technology, to students of all ages and backgrounds, as well as the society at large. The research plan includes the study of: (i) nonconvex quadratic programs, which, though very difficult to solve, encompass many problems arising, for example, in production and logistics, facility layout, circuit design, image partitioning, frequency assignment in networks, protein structure identification, and combinatorial optimization; (ii) linear programs over convex cones, which are one of the main tools to solve nonconvex quadratic programs, while being applicable to many situations in their own right (for example, in stock analysis, inventory theory, control theory, matrix analysis, truss topology design, and quantum chemistry). Because applications in these areas typically give rise to large-scale optimization problems that challenge today's algorithms and methodologies, this project develops new approaches (e.g., through advanced computational techniques and algorithmic development) for solving problems either exactly or approximately and applies them to specific applications. Educational activities of the project include: (i) outreach efforts to strengthen K-12 education, engage the community, and encourage the participation of underrepresented groups in computer science and information technology; (ii) course development activities that provide modern, high-quality instruction in optimization and related disciplines for undergraduate, graduate, and professional students. Efforts are appropriately targeted to the experience and background of the intended audience and are aligned with the goals of larger university, state, and federal institutions.