Last Updated：2025/12/31
Sentence
We
consider
two
different
variational
models
of
transport
networks,
the
so-called
branched
transport
problem
and
the
urban
planning
problem.
Based
on
a
novel
relation
to
Mumford-Shah
image
inpainting
and
techniques
developed
in
that
field,
we
show
for
a
two-dimensional
situation
that
both
highly
non-convex
network
optimisation
tasks
can
be
transformed
into
a
minorising
convex
variational
problem.
Quizzes for review
We consider two different variational models of transport networks, the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field, we show for a two-dimensional situation that both highly non-convex network optimisation tasks can be transformed into a minorising convex variational problem.
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English - English
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