CAREER: Large-Scale Semidefinite Programming

University Of Maryland Baltimore County, Baltimore MD

Investigators

Abstract

Nayakkankuppam This project, which lies at the interface of optimization theory, numerical analysis and parallel scientific computing, focuses on the design, analysis and implementation of novel algorithms for large-scale semidefinite programming. A growing number of applications (for example, structural design, communication networks, combinatorial optimization, quantum chemistry, VLSI design) give rise to very large-scale problems well beyond the capabilities of the interior-point algorithms currently in use. The investigator studies (a) quasi-Newton techniques in first and second order subgradient bundle methods, and (b) parallel variable distribution in interior-point and subgradient bundle methods. The goals of the project are three-fold: (i) to develop convergence theories for these new classes of algorithms, (ii) to develop fast, reliable and parallel software implementations, and (iii) to apply these algorithms and codes to specific problems in quantum chemistry and numerical linear algebra. The educational plan, integrated with the research goals of the project, includes (i) the development of new graduate curricula in parallel computing, numerical optimization and convex programming designed to train graduate students to participate in, and contribute to, the research program; (ii) a revision of undergraduate curricula in linear and nonlinear programming to include significant modeling and computational components. Due to the wide-ranging applicability of semidefinite programming, the tools and techniques developed in this project can directly benefit society by providing improved, cost-effective solutions to a variety of engineering design problems. The specific problems targeted in numerical linear algebra are relevant to aerospace applications, while the problems in quantum chemistry are of a fundamental nature with potential technological impact in, for example, semiconductor design, magnetic storage media, rational drug design, etc. The outreach activities of the project promote synergistic collaborations with a national lab and industry. The educational plan enriches special UMBC programs targeted at educating minorities and historically underrepresented groups.