Shape Optimization under Uncertainty from a Stochastic Programming Point of View

  • Authors
  • Harald Held

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Harald Held
    Pages 1-24
  3. Harald Held
    Pages 25-47
  4. Harald Held
    Pages 49-75
  5. Harald Held
    Pages 77-100
  6. Harald Held
    Pages 101-119
  7. Back Matter
    Pages 121-134

About this book


Optimization problems are relevant in many areas of technical, industrial, and economic applications. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization.

Harald Held considers an elastic body subjected to uncertain internal and external forces. Since simply averaging the possible loadings will result in a structure that might not be robust for the individual loadings, he uses techniques from level set based shape optimization and two-stage stochastic programming. Taking advantage of the PDE’s linearity, he is able to compute solutions for an arbitrary number of scenarios without significantly increasing the computational effort. The author applies a gradient method using the shape derivative and the topological gradient to minimize, e.g., the compliance . and shows that the obtained solutions strongly depend on the initial guess, in particular its topology. The stochastic programming perspective also allows incorporating risk measures into the model which might be a more appropriate objective in many practical applications.


PDE Programming Shape Optimization Stochastic Topology loadings optimization

Bibliographic information