Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accelerated Schemes For A Class of Variational Inequalities   We propose a novel method, namely the accelerated mirror-prox (AMP) method,
for computing the weak solutions of a class of deterministic and stochastic
monotone variational inequalities (VI). The main idea of this algorithm is to
incorporate a multi-step acceleration scheme into the mirror-prox method. For
both deterministic and stochastic VIs, the developed AMP method computes the
weak solutions with optimal rate of convergence. In particular, if the monotone
operator in VI consists of the gradient of a smooth function, the rate of
convergence of the AMP method can be accelerated in terms of its dependence on
the Lipschitz constant of the smooth function. For VIs with bounded feasible
sets, the estimate of the rate of convergence of the AMP method depends on the
diameter of the feasible set. For unbounded VIs, we adopt the modified gap
function introduced by Monteiro and Svaiter for solving monotone inclusion, and
demonstrate that the rate of convergence of the AMP method depends on the
distance from the initial point to the set of strong solutions.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph