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    PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance

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    Author
    Chernikov, Dmitry
    Issue Date
    2017
    Keywords
    adjoint differentiation
    automatic differentiation
    multiphysics
    nonlinear optimization
    optimization of portfolio of options
    PDE-constrained optimization
    Advisor
    Krokhmal, Pavlo
    Zhupanska, Olesya
    
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    Publisher
    The University of Arizona.
    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.
    Abstract
    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.
    Type
    text
    Electronic Dissertation
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Graduate College
    Systems & Industrial Engineering
    Degree Grantor
    University of Arizona
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