n this paper, we propose a class of inexact proximal point algorithms with relative error criterion for solving monotone variational inequalities. The next iterate in the proposed methods can be obtained in two ways. Under general hypothetical conditions, the global convergence of the new algorithms is established. By choosing a special form for the error, the proposed inexact proximal point algorithms reduce to a class of projection and contraction methods with linesearch, which reveals the connection between inexact proximal point algorithms and a class of projection methods. Numerical experiments demonstrate the efficiency of the new methods.
CUI Hengxin
,
JIANG Fan
. Inexact proximal point algorithms and projection methods for monotone variational inequalities[J]. Operations Research Transactions, 2026
, 30(2)
: 194
-208
.
DOI: 10.15960/j.cnki.issn.1007-6093.2026.02.015
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