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The aim of this paper is to establish a theory of Galerkin approximations tothe space of convex and compact subsets of $\R^d$ with favorable properties,both from a theoretical and from a computational perspective. These Galerkinspaces are first explored in depth and then used to solve optimization problemsin the space of convex and compact subsets of $\R^d$ approximately.

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