Auxiliary Problem Principle and Proximal Point Methods |
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Authors: | A Kaplan R Tichatschke |
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Institution: | (1) Department of Mathematics, University of Trier, Trier, Germany |
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Abstract: | An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension concerns the case that the operator is split into the sum of a single-valued operator
, possessing a kind of pseudo Dunn property, and a maximal monotone operator
. The current auxiliary problem is k constructed by fixing
at the previous iterate, whereas
(or its single-valued approximation
k) k is considered at a variable point. Using auxiliary operators of the form
k+
, with k>0, the standard for the auxiliary problem principle assumption of the strong convexity of the function h can be weakened exploiting mutual properties of
and h. Convergence of the general scheme is analyzed and some applications are sketched briefly. |
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Keywords: | Auxiliary problem principle Convex and nonconvex optimization Ill-posed problems Proximal point methods Regularization Variational inequalities |
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