Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient quadratic penalization through the partial minimization
  technique   Common computational problems, such as parameter estimation in dynamic models
and PDE constrained optimization, require data fitting over a set of auxiliary
parameters subject to physical constraints over an underlying state. Naive
quadratically penalized formulations, commonly used in practice, suffer from
inherent ill-conditioning. We show that surprisingly the partial minimization
technique regularizes the problem, making it well-conditioned. This viewpoint
sheds new light on variable projection techniques, as well as the penalty
method for PDE constrained optimization, and motivates robust extensions. In
addition, we outline an inexact analysis, showing that the partial minimization
subproblem can be solved very loosely in each iteration. We illustrate the
theory and algorithms on boundary control, optimal transport, and parameter
estimation for robust dynamic inference.

25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics