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![]() | New insights into one-norm solvers from the Pareto curve | ![]() |
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Figure 1 gives a schematic illustration
of a Pareto curve. The curve traces the optimal tradeoff between
and
for a
specific pair of
and
in
equation 1. Point
clarifies
the connection between the three parameters of QP
,
BP
, and LS
. The coordinates of a point on the Pareto
curve are
and the slope of the tangent at this point
is
. The end points of the curve--points
and
--are
two special cases. When
, the solution of LS
is
(point
). It coincides with
the solutions of BP
with
and
QP
with
. (The
infinity norm
is given by
.) When
, the solution of
BP
(point
) coincides with the
solutions of LS
, where
is the one norm of the solution,
and QP
, where
--i.e.,
infinitely
close to zero from above. These relations are formalized as follows
in van den Berg and Friedlander (2008):
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pcurve
Figure 1. Schematic illustration of a Pareto curve. Point ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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![]() | New insights into one-norm solvers from the Pareto curve | ![]() |
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