Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A "joint+marginal" approach to parametric polynomial optimization   Given a compact parameter set $Y\subset R^p$, we consider polynomial
optimization problems $(P_y$) on $R^n$ whose description depends on the
parameter $y\inY$. We assume that one can compute all moments of some
probability measure $\phi$ on $Y$, absolutely continuous with respect to the
Lebesgue measure (e.g. $Y$ is a box or a simplex and $\phi$ is uniformly
distributed). We then provide a hierarchy of semidefinite relaxations whose
associated sequence of optimal solutions converges to the moment vector of a
probability measure that encodes all information about all global optimal
solutions $x^*(y)$ of $P_y$. In particular, one may approximate as closely as
desired any polynomial functional of the optimal solutions, like e.g. their
$\phi$-mean. In addition, using this knowledge on moments, the measurable
function $y\mapsto x^*_k(y)$ of the $k$-th coordinate of optimal solutions, can
be estimated, e.g. by maximum entropy methods. Also, for a boolean variable
$x_k$, one may approximate as closely as desired its persistency
$\phi(\{y:x^*_k(y)=1\})$, i.e. the probability that in an optimal solution
$x^*(y)$, the coordinate $x^*_k(y)$ takes the value 1. At last but not least,
from an optimal solution of the dual semidefinite relaxations, one provides a
sequence of polynomial (resp. piecewise polynomial) lower approximations with
$L_1(\phi)$ (resp. almost uniform) convergence to the optimal value function.

8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc