The National Science Foundation (NSF) awarded a $275,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to George Mason University to develop innovative optimization algorithms and digital twin technologies. The project aims to advance mathematical methods for solving non-linear, non-smooth optimization problems constrained by partial differential equations, with applications in areas like pathogen propagation modeling, biomedical engineering, and structural integrity analysis. The research will focus on developing adaptive semismooth Newton and trust-region methods, primal-dual algorithms for risk-averse optimization, and structure-preserving finite element discretization techniques. The results will be disseminated through publications and presentations to benefit the broader scientific community. A Ph.D. student will also be supported through this grant. The project period runs from August 1, 2024 to July 31, 2027.
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