Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrange Multipliers, (Exact) Regularization and Error Bounds for
  Monotone Variational Inequalities   We examine two central regularization strategies for monotone variational
inequalities, the first a direct regularization of the operative monotone
mapping, and the second via regularization of the associated dual gap function.
A key link in the relationship between the solution sets to these various
regularized problems is the idea of exact regularization, which, in turn, is
fundamentally associated with the existence of Lagrange multipliers for the
regularized variational inequality. A regularization is said to be exact if a
solution to the regularized problem is a solution to the unregularized problem
for all parameters beyond a certain value. The Lagrange multipliers
corresponding to a particular regularization of a variational inequality, on
the other hand, are defined via the dual gap function. Our analysis suggests
various conceptual, iteratively regularized numerical schemes, for which we
provide error bounds, and hence stopping criteria, under the additional
assumption that the solution set to the unregularized problem is what we call
weakly sharp of order greater than one.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg