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Optimization Methods for Inverse Problems
Optimization plays an important role in solving many inverse problems.
Indeed, the task of inversion often either involves or is fully cast as a
solution of an optimization problem. In this light, the mere non-linear,
non-convex, and large-scale nature of many of these inversions gives rise to
some very challenging optimization problems. The inverse problem community has
long been developing various techniques for solving such optimization tasks.
However, other, seemingly disjoint communities, such as that of machine
learning, have developed, almost in parallel, interesting alternative methods
which might have stayed under the radar of the inverse problem community. In
this survey, we aim to change that. In doing so, we first discuss current
state-of-the-art optimization methods widely used in inverse problems. We then
survey recent related advances in addressing similar challenges in problems
faced by the machine learning community, and discuss their potential advantages
for solving inverse problems. By highlighting the similarities among the
optimization challenges faced by the inverse problem and the machine learning
communities, we hope that this survey can serve as a bridge in bringing
together these two communities and encourage cross fertilization of ideas.Comment: 13 page
A class of multi-phase traffic theories for microscopic, kinetic and continuum traffic models
In the present paper a review and numerical comparison of a special class of
multi-phase traffic theories based on microscopic, kinetic and macroscopic
traffic models is given. Macroscopic traffic equations with multi-valued
fundamental diagrams are derived from different microscopic and kinetic models.
Numerical experiments show similarities and differences of the models, in
particular, for the appearance and structure of stop and go waves for highway
traffic in dense situations. For all models, but one, phase transitions can
appear near bottlenecks depending on the local density and velocity of the
flow
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