ISyE Seminar - Johannes Milz

Event Details
  • Date/Time:
    • Thursday January 27, 2022
      11:00 am - 12:00 pm
  • Location: Groseclose 402
  • Phone:
  • URL: ISyE Building
  • Email:
  • Fee(s):
    N/A
  • Extras:
Contact
No contact information submitted.
Summaries

Summary Sentence: Properties of Monte Carlo Estimators for Risk-Neutral PDE-Constrained Optimization Problems

Full Summary:

Abstract:

Complex systems in science and engineering can often be modeled with partial differential equations (PDEs) with uncertain parameters. In order to improve the design of such systems, we formulate a risk-neutral optimization problem with PDE constraints, an infinite-dimensional stochastic program. We apply the sample average approximation (SAA) to the risk-neutral PDE-constrained optimization problem and analyze the consistency of the SAA optimal value and solutions. Our analysis exploits hidden compactness in PDE-constrained optimization problems, allowing us to construct deterministic, compact sets containing the solutions to the risk-neutral problem and those to the SAA problems. Exploiting further problem structure, we establish nonasymptotic sample size estimates using the covering number approach, thereby we shed light on the computational resources needed to obtain accurate solutions.

Title:

Properties of Monte Carlo Estimators for Risk-Neutral PDE-Constrained Optimization Problems

Abstract:

Complex systems in science and engineering can often be modeled with partial differential equations (PDEs) with uncertain parameters. In order to improve the design of such systems, we formulate a risk-neutral optimization problem with PDE constraints, an infinite-dimensional stochastic program. We apply the sample average approximation (SAA) to the risk-neutral PDE-constrained optimization problem and analyze the consistency of the SAA optimal value and solutions. Our analysis exploits hidden compactness in PDE-constrained optimization problems, allowing us to construct deterministic, compact sets containing the solutions to the risk-neutral problem and those to the SAA problems. Exploiting further problem structure, we establish nonasymptotic sample size estimates using the covering number approach, thereby we shed light on the computational resources needed to obtain accurate solutions.

Bio:

Johannes Milz is research associate at the Technical University of Munich. Johannes' research broadly lies in optimization under uncertainty with a current focus on complexity analysis of and algorithmic design for PDE-constrained optimization problems under uncertainty. He received his doctorate in applied mathematics from the Technical University of Munich in 2021.

Additional Information

In Campus Calendar
Yes
Groups

School of Industrial and Systems Engineering (ISYE)

Invited Audience
Faculty/Staff, Postdoc, Public, Graduate students, Undergraduate students
Categories
Seminar/Lecture/Colloquium
Keywords
No keywords were submitted.
Status
  • Created By: Julie Smith
  • Workflow Status: Published
  • Created On: Jan 14, 2022 - 10:02am
  • Last Updated: Jan 14, 2022 - 10:02am