Abstract
In this paper, we introduce two general iterative methods for a certain optimization problem of which the constrained set is the common set of the solution set of the variational inequality problem for a continuous monotone mapping and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Under some control conditions, we establish the strong convergence of the proposed methods to a common element of the solution set and the fixed point set, which is the unique solution of a certain optimization problem. As a direct consequence, we obtain the unique minimum-norm common point of the solution set and the fixed point set.
Highlights
Let H be a real Hilbert space with the inner product ·, · and the induced norm ·
Under well-known control conditions on the sequence {αn} ⊂ [, ], they proved the strong convergence of the sequence {xn} generated by ( . ) to a point x ∈ Fix(S), which is the unique solution of the variational inequality (A – γ f )x, x – p ≤, ∀p ∈ Fix(S), which is the optimality condition for the optimization problem min Ax, x – h(x), x∈Fix(S)
Under different control conditions on the sequence {αn} ⊂ [, ] and the sequence {xn} generated by ( . ), he showed the strong convergence of the sequence {xn} to a point x ∈ Fix(T), which is the unique solution of the optimization problem min μ
Summary
Let H be a real Hilbert space with the inner product ·, · and the induced norm ·. ) coupled with the fixed point problem, many authors have introduced some iterative methods for finding an element of VI(C, F) ∩ Fix(S), where F is an α-inverse-strongly monotone mapping and {xt} converges strongly as t → to a point x ∈ VI(C, F), where is the unique solution of the optimization problem min μ x∈VI(C,F)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
