Advances in the design of algorithms for solving data science and large-scale, complex decision-making problems are paramount in modern-day scientific innovation. At the core of such algorithms is mathematical optimization, a particular strength of many of the faculty members in the Department of ISE at Lehigh. Lehigh ISE faculty members Frank E. Curtis and Daniel P. Robinson, in collaboration with Albert S. Berahas at the University of Michigan, have been awarded a three-year half-million dollar award from the Office of Naval Research (ONR) to design and analyze next-generation algorithms for solving problems aligned with the interests of ONR’s Mathematics, Computer and Information Sciences (MCIS) Division.
For this project, the Lehigh and Michigan team will design, analyze, implement, and test algorithms designed to solve optimization problems involving stochastic objective functions and deterministic constraints. Despite recent advances in the context of solving unconstrained stochastic optimization problems—which includes the excitement around training deep neural networks (DNNs) for machine learning applications—relatively little has been accomplished in the constrained setting, despite the fact that constraints arise naturally in many applications of interest. Curtis, Robinson, and their faculty, postdoctoral, and student collaborators will leverage their expertise on stochastic nonlinear optimization to forge new classes of numerical methods for solving these cutting-edge problems.
Frank: "We're extremely excited to receive this support from ONR and look forward to this project, which we expect to lead to new algorithms and techniques that will inspire others in the community to tackle these very challenging and important types of problems."