Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Minimal Displacement Vector of the Douglas-Rachford Operator   The Douglas-Rachford algorithm can be represented as the fixed point
iteration of a firmly nonexpansive operator. When the operator has no fixed
points, the algorithm's iterates diverge, but the difference between
consecutive iterates converges to the so-called minimal displacement vector,
which can be used to certify infeasibility of an optimization problem. In this
paper, we establish new properties of the minimal displacement vector, which
allow us to generalize some existing results.

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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con