Portland State University. Department of Mathematics and Statistics
Mau Nam Nguyen
Date of Award
Doctor of Philosophy (Ph.D.) in Mathematical Sciences
1 online resource (viii, 132 pages)
This thesis contains contributions in three areas: the theory of generalized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geometric approach is used to advance the theory and tools used for studying generalized notions of derivatives for nonsmooth functions. These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions. A strong understanding of the subdifferential is essential for numerical optimization algorithms, which are developed and applied to nonsmooth problems in operations research, including non-convex problems. Finally, an optimization framework is applied to solve a problem in electric power systems involving a smart solar inverter and battery storage system providing energy and ancillary services to the grid.
Rector, Robert Blake Hayden, "Generalized Differential Calculus and Applications to Optimization" (2017). Dissertations and Theses. Paper 3627.