Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arnoldi-based Sampling for High-dimensional Optimization using Imperfect
  Data   We present a sampling strategy suitable for optimization problems
characterized by high-dimensional design spaces and noisy outputs. Such outputs
can arise, for example, in time-averaged objectives that depend on chaotic
states. The proposed sampling method is based on a generalization of Arnoldi's
method used in Krylov iterative methods. We show that Arnoldi-based sampling
can effectively estimate the dominant eigenvalues of the underlying Hessian,
even in the presence of inaccurate gradients. This spectral information can be
used to build a low-rank approximation of the Hessian in a quadratic model of
the objective. We also investigate two variants of the linear term in the
quadratic model: one based on step averaging and one based on directional
derivatives. The resulting quadratic models are used in a trust-region
optimization framework called the Stochastic Arnoldi's Method (SAM). Numerical
experiments highlight the potential of SAM relative to conventional
derivative-based and derivative-free methods when the design space is
high-dimensional and noisy.

18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics