In this dissertation we investigate methods of solving various optimization problems with PDE constraints, i.e. optimization problems that have a system of partial differential equations in the set of constraints, and develop frameworks for a number of practically inspired problems that were not considered in the literature before. Such problems arise in areas like fluid mechanics, chemical engineering, finance, and other areas where a physical system needs to be optimized. In most of the literature sources on PDE-constrained optimization only relatively simple systems of PDEs are considered, they are either linear, or the size of the system is small. On the contrary, in our case, we search for solution methods to problems constrained by large (8 to 10 equations) and non-linear systems of PDEs.
More specifically, in the first part of the dissertation we consider a multiphysics phenomenon where electromagnetic and mechanical fields interact within an electrically conductive body,
and develop the optimization framework to find an efficient way to control one field through another.
We also apply the developed PDE-constrained optimization framework to a financial options portfolio optimization problem, and more specifically consider the case that to the best of our knowledge is not covered in the literature.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/626368 |
| Date | January 2017 |
| Creators | Chernikov, Dmitry, Chernikov, Dmitry |
| Contributors | Krokhmal, Pavlo, Zhupanska, Olesya, Krokhmal, Pavlo, Zhupanska, Olesya, Zhang, Hao, Furfaro, Roberto |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Electronic Dissertation |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
Page generated in 0.004 seconds