Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Majorization-Minimization-Based Levenberg--Marquardt Method for
  Constrained Nonlinear Least Squares   A new Levenberg--Marquardt (LM) method for solving nonlinear least squares
problems with convex constraints is described. Various versions of the LM
method have been proposed, their main differences being in the choice of a
damping parameter. In this paper, we propose a new rule for updating the
parameter so as to achieve both global and local convergence even under the
presence of a convex constraint set. The key to our results is a new
perspective of the LM method from majorization-minimization methods.
Specifically, we show that if the damping parameter is set in a specific way,
the objective function of the standard subproblem in LM methods becomes an
upper bound on the original objective function under certain standard
assumptions.
  Our method solves a sequence of the subproblems approximately using an
(accelerated) projected gradient method. It finds an $\epsilon$-stationary
point after $O(\epsilon^{-2})$ computation and achieves local quadratic
convergence for zero-residual problems under a local error bound condition.
Numerical results on compressed sensing show that our method converges faster
in many cases than existing LM methods and the projected gradient method.

10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: stat
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn