A generalized Halpern-type forward-backward splitting algorithm for solving variational inclusion problems
Copyright policy )A generalized Halpern-type forward-backward splitting algorithm for solving variational inclusion problems
<abstract><p>In this paper, we investigate the problem of finding a zero of sum of two accretive operators in the setting of uniformly convex and $ q $-uniformly smooth real Banach spaces ($ q > 1 $). We incorporate the inertial and relaxation parameters in a Halpern-type forward-backward splitting algorithm to accelerate the convergence of its sequence to a zero of sum of two accretive operators. Furthermore, we prove strong convergence of the sequence generated by our proposed iterative algorithm. Finally, we provide a numerical example in the setting of the classical Banach space $ l_4(\mathbb{R}) $ to study the effect of the relaxation and inertial parameters in our proposed algorithm.</p></abstract>
- China Medical University Hospital Taiwan
- Burapha University Thailand
- China Medical University China (People's Republic of)
- Near East University
- African Institute of Science and Technology Nigeria
Inverse Problems in Mathematical Physics and Imaging, Convex Optimization, Quadratic Programming, Economics, Geometry, generalized duality mapping, Quantum mechanics, Social psychology, Relaxation (psychology), QA1-939, FOS: Mathematics, Genetics, Psychology, accretive operator, Biology, Mathematical Physics, Economic growth, Numerical Analysis, convergence, Banach space, Numerical Optimization Techniques, Ecology, Physics, Zero (linguistics), Pure mathematics, Linguistics, Iterative Algorithms for Nonlinear Operators and Optimization, Discrete mathematics, Applied mathematics, FOS: Philosophy, ethics and religion, relaxation parameter, Regular polygon, Algorithm, FOS: Psychology, Philosophy, Computational Theory and Mathematics, splitting method, FOS: Biological sciences, Computer Science, Physical Sciences, Convergence (economics), FOS: Languages and literature, Inertial frame of reference, Type (biology), Mathematics, Sum of Squares Techniques, Sequence (biology)
Inverse Problems in Mathematical Physics and Imaging, Convex Optimization, Quadratic Programming, Economics, Geometry, generalized duality mapping, Quantum mechanics, Social psychology, Relaxation (psychology), QA1-939, FOS: Mathematics, Genetics, Psychology, accretive operator, Biology, Mathematical Physics, Economic growth, Numerical Analysis, convergence, Banach space, Numerical Optimization Techniques, Ecology, Physics, Zero (linguistics), Pure mathematics, Linguistics, Iterative Algorithms for Nonlinear Operators and Optimization, Discrete mathematics, Applied mathematics, FOS: Philosophy, ethics and religion, relaxation parameter, Regular polygon, Algorithm, FOS: Psychology, Philosophy, Computational Theory and Mathematics, splitting method, FOS: Biological sciences, Computer Science, Physical Sciences, Convergence (economics), FOS: Languages and literature, Inertial frame of reference, Type (biology), Mathematics, Sum of Squares Techniques, Sequence (biology)
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