The meeting will bring together about 50 mathematicians from
- Real Algebraic Geometry (sums of squares),
- Functional Analysis (moment problems) and
- Optimization (interior point methods).
New surprising answers on the two questions
- which polynomials posess certain certificates of positivity
(often
involving sums of squares of polynomials) and
- which linear forms on the polynomial ring are integration with
respect
to a measure (moment problem)
have been given by people from Functional Analysis and Real Algebraic
Geometry
in the last 15 years. The two problems amount to study
infinite-dimensional
cones of positive polynomials from viewpoints dual to each other.
About 5 years ago, people from Optimization recognized the practical
impact
of these work on polynomial optimization problems. Since then, a third,
asymptotical
viewpoint of these infinite-dimensional cones as limit of
finite-dimensional
cones of growing dimension has been added. The above mentioned duality
becomes
now manifest in a concrete duality of convex optimization problems
which
can be solved by interior point methods.
The subject of the conference is the interplay of these different
viewpoints
of positive polynomials. The spirit will be very similar to the 2002
Oberwolfach
workshop "Positivität von Polynomen". We recommend to look at its report
(ps file) to get a good idea.
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