Efficient Stochastic Descent Methods for PDE-Constrained Optimization with Uncertain Coefficients

Feineis, Calvin

Efficient Stochastic Descent Methods for PDE-Constrained Optimization with Uncertain Coefficients

Dateien

Feineis_2-171a3bcqba3tk2.pdfGröße: 1.36 MBDownloads: 227

Datum

2021

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Masterarbeit/Diplomarbeit

Publikationsstatus

Published

Zusammenfassung

In this thesis, we consider a convex, elliptic PDE-constrained optimal control problem that is subject to uncertainty. To solve this problem numerically we use three stochastic descent methods, namely the Stochastic Gradient method, the Stochastic Variance Reduced Gradient method and the Stochastic Adaptive Sampling method. We state theoretical convergence results for the three stochastic descent methods and present a setting in which we conduct numerical tests to compare the convergence behaviour and the CPU time. The numerical experiments show that a modification of the Stochastic Adaptive Sampling method in combination with the Barzilai-Borwein step size rule is the superior choice for the specific problem.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Stochastic Descent Methods, PDE-Constrained Optimization, Stochastic Gradient, PDE with uncertain coefficients, Stochastic Optimization

Zitieren

ISO 690

FEINEIS, Calvin, 2021. Efficient Stochastic Descent Methods for PDE-Constrained Optimization with Uncertain Coefficients [Master thesis]. Konstanz: Universität Konstanz

BibTex

@mastersthesis{Feineis2021Effic-53934,
  year={2021},
  title={Efficient Stochastic Descent Methods for PDE-Constrained Optimization with Uncertain Coefficients},
  address={Konstanz},
  school={Universität Konstanz},
  author={Feineis, Calvin}
}

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Hochschulschriftenvermerk

Konstanz, Universität Konstanz, Masterarbeit/Diplomarbeit, 2021

Universitätsbibliographie

Nein