Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical points via monodromy and local methods   In many areas of applied mathematics and statistics, it is a fundamental
problem to find the best representative of a model by optimizing an objective
function. This can be done by determining critical points of the objective
function restricted to the model.
  We compile ideas arising from numerical algebraic geometry to compute the
critical points of an objective function. Our method consists of using
numerical homotopy continuation and a monodromy action on the total critical
space to compute all of the complex critical points of an objective function.
To illustrate the relevance of our method, we apply it to the Euclidean
distance function to compute ED-degrees and the likelihood function to compute
maximum likelihood degrees.

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The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph