Many methods have been proposed in the literature for solving the split variational inequality problem.Most of these methods either require that this problem is transformed into an equivalent variational inequality pr...Many methods have been proposed in the literature for solving the split variational inequality problem.Most 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 co-coercive.However,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 problem.On the other hand,the co-coercive assumption of the underlying operators would preclude the potential applications of these methods.To 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 assumption.The 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 speed.Moreover,the sequence generated by these methods is shown to converge strongly to a minimum-norm solution of the problem in real Hilbert spaces.Furthermore,numerical implementations and comparisons are given to support our theoretical findings.展开更多
In the present work the analysis of the basic methods for solving typical geometrical engineering problems is made.The basic problem is revealed and the first-level tasks of its solution are defined.A general algorith...In the present work the analysis of the basic methods for solving typical geometrical engineering problems is made.The basic problem is revealed and the first-level tasks of its solution are defined.A general algorithm for solving typical geometrical problems in the form of standardized logical blocks is offered.The general algorithm for the solution of typical geometrical problems is discussed,taking into account the iterative nature of the proposed methods.The introduced formal general algorithm allows students to master their skills of independent work.Practical engineers can use the developed general approach for solving new difficult real-world problems.Synthesized general algorithm,as the main contribution to geometry,allows,on deductive basis—“from the general to quotient”,to teach and study engineering geometry.展开更多
基金supported by the University of KwaZulu-Natal(UKZN)Doctoral Scholarshipsupported by the National Research Foundation(NRF)South Africa(S&F-DSI/NRF Free Standing Postdoctoral Fellowship(120784)supported by the National Research Foundation(NRF)South Africa Incentive Funding for Rated Researchers(119903).
文摘Many methods have been proposed in the literature for solving the split variational inequality problem.Most 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 co-coercive.However,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 problem.On the other hand,the co-coercive assumption of the underlying operators would preclude the potential applications of these methods.To 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 assumption.The 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 speed.Moreover,the sequence generated by these methods is shown to converge strongly to a minimum-norm solution of the problem in real Hilbert spaces.Furthermore,numerical implementations and comparisons are given to support our theoretical findings.
文摘In the present work the analysis of the basic methods for solving typical geometrical engineering problems is made.The basic problem is revealed and the first-level tasks of its solution are defined.A general algorithm for solving typical geometrical problems in the form of standardized logical blocks is offered.The general algorithm for the solution of typical geometrical problems is discussed,taking into account the iterative nature of the proposed methods.The introduced formal general algorithm allows students to master their skills of independent work.Practical engineers can use the developed general approach for solving new difficult real-world problems.Synthesized general algorithm,as the main contribution to geometry,allows,on deductive basis—“from the general to quotient”,to teach and study engineering geometry.
