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A Galerkin approach to optimization in the space of convex and compact subsets of $${\mathbb {R}}^d$$ R d

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  • Janosch Rieger

    (Monash University)

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 $${\mathbb {R}}^d$$ R d 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 $${\mathbb {R}}^d$$ R d approximately.

Suggested Citation

  • Janosch Rieger, 2021. "A Galerkin approach to optimization in the space of convex and compact subsets of $${\mathbb {R}}^d$$ R d," Journal of Global Optimization, Springer, vol. 79(3), pages 593-615, March.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:3:d:10.1007_s10898-020-00941-9
    DOI: 10.1007/s10898-020-00941-9
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    References listed on IDEAS

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    1. David G. Luenberger & Yinyu Ye, 2016. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 4, number 978-3-319-18842-3, September.
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    Cited by:

    1. Andreas Ernst & Lars Grüne & Janosch Rieger, 2023. "A linear programming approach to approximating the infinite time reachable set of strictly stable linear control systems," Journal of Global Optimization, Springer, vol. 86(2), pages 521-543, June.

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