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At the Intersection of Differential ...

Gilles, Marc Aurele Tiberius.

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At the Intersection of Differential Equations and Optimization: Inverse Problems, Path Planning and Krylov Subspaces.

Record Type:	Electronic resources : Monograph/item
Title/Author:	At the Intersection of Differential Equations and Optimization: Inverse Problems, Path Planning and Krylov Subspaces./
Author:	Gilles, Marc Aurele Tiberius.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	179 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
Contained By:	Dissertations Abstracts International80-12B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13883339
ISBN:	9781392248935

At the Intersection of Differential Equations and Optimization: Inverse Problems, Path Planning and Krylov Subspaces.
Gilles, Marc Aurele Tiberius.

At the Intersection of Differential Equations and Optimization: Inverse Problems, Path Planning and Krylov Subspaces. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 179 p.

Source: Dissertations Abstracts International, Volume: 80-12, Section: B.

Thesis (Ph.D.)--Cornell University, 2019.

This item must not be sold to any third party vendors.

Four problems at the intersection of optimization and partial differential equations are presented. First, a problem in remote sensing of the marine atmospheric boundary layer is discussed. A method that exploits the low-rank structure of the electromagnetic field is used to infer the refractive index profile of the lower atmosphere. The second problem is concerned with 3D X-ray imaging of large objects at nanometer scale resolution. A massively parallel optimization method is used to perform the reconstruction from measurements of an object outside of the depth of focus. The third problem presents a path planning problem where an evader is choosing his trajectory to hinder the surveillance of an observer. An algorithm to compute optimal strategies using ideas from convex optimization, game theory and optimal control is described. The final chapter presents a practical framework to apply Krylov subspace methods to differential operators.

ISBN: 9781392248935Subjects--Topical Terms:

1669109
Applied Mathematics.

At the Intersection of Differential Equations and Optimization: Inverse Problems, Path Planning and Krylov Subspaces.
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100 1 $a Gilles, Marc Aurele Tiberius. $3 3437967
245 1 0 $a At the Intersection of Differential Equations and Optimization: Inverse Problems, Path Planning and Krylov Subspaces.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 179 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Townsend, Alex.
502 $a Thesis (Ph.D.)--Cornell University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a Four problems at the intersection of optimization and partial differential equations are presented. First, a problem in remote sensing of the marine atmospheric boundary layer is discussed. A method that exploits the low-rank structure of the electromagnetic field is used to infer the refractive index profile of the lower atmosphere. The second problem is concerned with 3D X-ray imaging of large objects at nanometer scale resolution. A massively parallel optimization method is used to perform the reconstruction from measurements of an object outside of the depth of focus. The third problem presents a path planning problem where an evader is choosing his trajectory to hinder the surveillance of an observer. An algorithm to compute optimal strategies using ideas from convex optimization, game theory and optimal control is described. The final chapter presents a practical framework to apply Krylov subspace methods to differential operators.
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650 4 $a Applied Mathematics. $3 1669109
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773 0 $t Dissertations Abstracts International $g 80-12B.
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856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13883339