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dc.contributor.authorNguyễn, Hiếu Thảo-
dc.date.accessioned2019-09-12T09:02:09Z-
dc.date.available2019-09-12T09:02:09Z-
dc.date.issued2018-
dc.identifier.urihttp://dspace.ctu.edu.vn/jspui/handle/123456789/12475-
dc.description.abstractThis paper proposes an algorithm for solving structured optimization problems, which covers both the backward–backward and the Douglas–Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the corresponding operator is characterized in several cases. Convergence criteria of the algorithm in terms of general fixed point iterations are established. When applied to nonconvex feasibility including potentially inconsistent problems, we prove local linear convergence results under mild assumptions on regularity of individual sets and of the collection of sets. In this special case, we refine known linear convergence criteria for the Douglas–Rachford (DR) algorithm. As a consequence, for feasibility problem with one of the sets being affine, we establish criteria for linear and sublinear convergence of convex combinations of the alternating projection and the DR methods. These results seem to be new. We also demonstrate the seemingly improved numerical performance of this algorithm compared to the RAAR algorithm for both consistent and inconsistent sparse feasibility problems.vi_VN
dc.language.isoenvi_VN
dc.relation.ispartofseriesComputational Optimization and Applications;70 .- p. 841-863-
dc.subjectAlmostaver agednessvi_VN
dc.subjectPicard iterationvi_VN
dc.subjectAlternating projection methodvi_VN
dc.subjectDouglas–Rachford methodvi_VN
dc.subjectRAAR algorithmvi_VN
dc.subjectKrasnoselski–Mann relaxationvi_VN
dc.subjectMetric subregularityvi_VN
dc.subjectTransversalityvi_VN
dc.subjectCollection of setsvi_VN
dc.titleA convergent relaxation of the Douglas–Rachford algorithmvi_VN
dc.typeArticlevi_VN
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