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Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1697-1726页

作者： Timilehin Opeyemi Alakoya oluwatosin temitope mewomo School of Mathematics Statistics and Computer ScienceUniversity of KwaZulu-NatalDurbanSouth Africa

In this paper,we study the concept of split monotone variational inclusion problem with multiple output *** propose a new relaxed inertial iterative method with self-adaptive step sizes for approximating the solution of the problem in the framework of Hilbert *** proposed algorithm does not require the co-coerciveness nor the Lipschitz continuity of the associated single-valued ***,some parameters are relaxed to accommodate a larger range of values for the step *** some mild conditions on the control parameters and without prior knowledge of the operator norms,we obtain strong convergence result for the proposed ***,we apply our result to study certain classes of optimization problems and we present several numerical experiments to demonstrate the implementability of the proposed *** of the existing results in the literature could be viewed as special cases of our result in this paper.

关键词： Split inverse problems non-Lipschitz operators inertial technique self-adaptive step sizes

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

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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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维普期刊数据库

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Further Investigation into Split Common Fixed Point Problem for Demicontractive Operators

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Acta Mathematica Sinica,English Series 2016年第11期32卷 1357-1376页

作者： Yekini SHEHU oluwatosin T.mewomo Department of Mathematics University of Nigeria School of Mathematics Statistics and Computer ScienceUniversity of Kwazulu Natal

Our contribution in this paper is to propose an iterative algorithm which does not reqmre prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common fixed point problem of demicontractive mappings in a real Hilbert space. So many authors have used algorithms involving the operator norm for solving split common fixed point problem, but as widely known the computation of these Mgorithms may be difficult and for this reason, authors have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. We introduce a new algorithm for solving the split common fixed point problem for demicontractive mappings with a way of selecting the step-sizes such that the implementation of the Mgorithm does not require the calculation or estimation of the operator norm and then prove strong convergence of the sequence in real Hilbert spaces. Finally, we give some applications of our result and numerical example at the end of the paper.

关键词： Demicontractive mappings split common fixed point problems iterative scheme strongconvergence Hilbert spaces

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