Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On The Strong Convergence of The Gradient Projection Algorithm with
  Tikhonov regularizing term   We investigate the strong and the weak convergence properties of the
following gradient projection algorithm with Tikhonov regularizing term \[
x_{n+1}=P_{Q}(x_{n}-\gamma_{n}\nabla f(x_{n})-\gamma_{n}\alpha_{n}\nabla \phi
(x_{n})), \] where $P_{Q}$ is the projection operator from a Hilbert space
$\mathcal{H}$ onto a given nonempty, closed and convex subset $Q,$
$f:\mathcal{H}% \rightarrow \mathbb{R}$ a regular convex function, $\phi
:\mathcal{H}% \rightarrow \mathbb{R}$ a regular strongly convex function, and
$\gamma_{n}$ and $\alpha_{n}$ are positive real numbers. Following a Lyuapunov
approach inspired essentially from the paper [Comminetti R, Peypouquet J Sorin
S. Strong asymptotic convergence of evolution equations governed by maximal
monotone operators with Tikhonov regularization. J. Differential Equations.
(2001); 245:3753-3763], we establish the strong convergence of $(x_{n})_{n}$ to
a particular minimizer $x^{\ast }$ of $f$ on $Q$ under some simple and natural
conditions on the objective function $f$\ and the sequences $(\gamma_{n})_{n}$
and $(\alpha_{n})_{n}$

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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg