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RELAXED INERTIAL METHODS FOR SOLVING SPLIT VARIATIONAL INEQUALITY PROBLEMS WITHOUT PRODUCT SPACE FORMULATION

Acta Mathematica Scientia 2022年第5期42卷 1701-1733页

作者： grace nnennaya ogwo Chinedu IZUCHUKWU Oluwatosin Temitope MEWOMO School of Mathematics Statistics and Computer ScienceUniversity of KwaZulu-NatalDurbanSouth Africa

Many methods have been proposed in the literature for solving the split variational inequality *** of these methods either require that this problem is transformed into an equivalent variational inequality problem in a product space,or that the underlying operators are ***,it has been discovered that such product space transformation may cause some potential difficulties during implementation and its approach may not fully exploit the attractive splitting nature of the split variational inequality *** the other hand,the co-coercive assumption of the underlying operators would preclude the potential applications of these *** avoid these setbacks,we propose two new relaxed inertial methods for solving the split variational inequality problem without any product space transformation,and for which the underlying operators are freed from the restrictive co-coercive *** methods proposed,involve projections onto half-spaces only,and originate from an explicit discretization of a dynamical system,which combines both the inertial and relaxation techniques in order to achieve high convergence ***,the sequence generated by these methods is shown to converge strongly to a minimum-norm solution of the problem in real Hilbert ***,numerical implementations and comparisons are given to support our theoretical findings.

关键词： split variational inequality problems relaxation technique inertial extrapolation minimum-norm solutions product space formulation half-spaces

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