Four Mathematical Programming Paradigms with Operations Research Applications

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

This proposal aims at investigating four emerging modeling paradigms in mathematical programming that have gained increased attention in recent years due to their pervasive applications in operations research and other engineering fields as well as in economics and finance, but which have yet to receive wide popularity and lack focused research. These paradigms are: competition, dynamics, hierarchy, and inverse problems. The objective of the project is to develop a comprehensive and rigorous foundation for the sustained treatment and applications of these paradigms in the context of complex engineering and economic systems. The proposed approach is to study the mathematical formulations of these paradigms in terms of extended mathematical and equilibrium programs, constrained continuous-time dynamical systems, and multi-agent and multi-level optimization. Novel mathematical theories and advanced computational tools will be developed. This will require the combined methodology of continuous and disjunctive programming, global optimization, continuous- and discrete-time dynamical systems theory, and contemporary mathematical tools such as variational and set-valued analysis. If successful, the results of the proposed research will lead to improved understanding and efficient solution of highly complex engineering, economic, and biological systems characterized by four intrinsic elements: competition among multiple selfish agents, time evolution prior to the attainment of an optimum or equilibrium, hierarchical structure of the optimizing agents, and historical and/or observed data that need to be respected. Due to its interdisciplinary nature, the proposed activity offers an opportunity to bring together experts in diverse disciplines to advance their individual fields and make joint contributions to significant societal problems such as efficient resource allocation in engineering and economic systems, congestion in transportation systems, and resolution of conflicts among competing selfish agents, to name a few areas of applications.