Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving Stochastic Optimization by Newton-type methods with
  Dimension-Adaptive Sparse Grid Quadrature   Stochastic optimisation problems minimise expectations of random cost
functions. We use 'optimise then discretise' method to solve stochastic
optimisation. In our approach, accurate quadrature methods are required to
calculate the objective, gradient or Hessian which are in fact integrals. We
apply the dimension-adaptive sparse grid quadrature to approximate these
integrals when the problem is high dimensional. Dimension-adaptive sparse grid
quadrature shows high accuracy and efficiency in computing an integral with a
smooth integrand. It is a kind of generalisation of the classical sparse grid
method, which refines different dimensions according to their importance. We
show that the dimension-adaptive sparse grid quadrature has better performance
in the optimise then discretise' method than the 'discretise then optimise'
method.

28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: funct-an
16
The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
3
The categories of this paper are: physics