A Galerkin approach to optimization in the space of convex and compact subsets of Rd

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Abstract

The aim of this paper is to open up a new perspective on set and shape optimization by establishing a theory of Galerkin approximations to the space of convex and compact subsets of Rd with favorable properties, both from a theoretical and from a computational perspective. Galerkin spaces consisting of polytopes with fixed facet normals are first explored in depth and then used to solve optimization problems in the space of convex and compact subsets of Rd approximately.

Original languageEnglish
Pages (from-to)593–615
Number of pages23
JournalJournal of Global Optimization
Volume79
DOIs
Publication statusPublished - 7 Aug 2020

Keywords

  • Convex sets
  • Galerkin approximation
  • Polytopes
  • Set optimization

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