Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unified Single-loop Alternating Gradient Projection Algorithm for
  Nonconvex-Concave and Convex-Nonconcave Minimax Problems   Much recent research effort has been directed to the development of efficient
algorithms for solving minimax problems with theoretical convergence guarantees
due to the relevance of these problems to a few emergent applications. In this
paper, we propose a unified single-loop alternating gradient projection (AGP)
algorithm for solving smooth nonconvex-(strongly) concave and (strongly)
convex-nonconcave minimax problems. AGP employs simple gradient projection
steps for updating the primal and dual variables alternatively at each
iteration. We show that it can find an $\varepsilon$-stationary point of the
objective function in $\mathcal{O}\left( \varepsilon ^{-2} \right)$ (resp.
$\mathcal{O}\left( \varepsilon ^{-4} \right)$) iterations under
nonconvex-strongly concave (resp. nonconvex-concave) setting. Moreover, its
gradient complexity to obtain an $\varepsilon$-stationary point of the
objective function is bounded by $\mathcal{O}\left( \varepsilon ^{-2} \right)$
(resp., $\mathcal{O}\left( \varepsilon ^{-4} \right)$) under the strongly
convex-nonconcave (resp., convex-nonconcave) setting. To the best of our
knowledge, this is the first time that a simple and unified single-loop
algorithm is developed for solving both nonconvex-(strongly) concave and
(strongly) convex-nonconcave minimax problems. Moreover, the complexity results
for solving the latter (strongly) convex-nonconcave minimax problems have never
been obtained before in the literature. Numerical results show the efficiency
of the proposed AGP algorithm. Furthermore, we extend the AGP algorithm by
presenting a block alternating proximal gradient (BAPG) algorithm for solving
more general multi-block nonsmooth nonconvex-(strongly) concave and (strongly)
convex-nonconcave minimax problems. We can similarly establish the gradient
complexity of the proposed algorithm under these four different settings.

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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat