1
25
semicontinuous functions
function
convergence theorem
convergence behavior
technique
Lipschitz
https://scigraph.springernature.com/explorer/license/
suitable control conditions
lower semicontinuous functions
theorem
convex minimization problem
accelerated algorithm
gradient
restoration problem
objective function
In this paper, we introduce and study a new accelerated algorithm based on forwardâ€“backward and SP-algorithm for solving a convex minimization problem of the sum of two convex and lower semicontinuous functions in a Hilbert space. Under some suitable control conditions, a weak convergence theorem of the proposed algorithm based on a fixed point is established. Moreover, we choose the stepsize of our algorithm which is independent on the Lipschitz constant of the gradient of the objective function by using a linesearch technique, and then a weak convergence result of the proposed algorithm is analyzed. As applications, we apply the proposed algorithm for solving the image restoration problems and compare its convergence behavior with other well-known algorithms in the literature. By our experiment, the algorithms have a higher efficiency than the others.
high efficiency
paper
article
weak convergence results
space
control condition
experiments
point
linesearch technique
image restoration problems
2022-03-17
2022-03-17
optimization algorithm
convex
efficiency
behavior
new accelerated algorithm
algorithm
sum
minimization problem
true
2022-10-01T06:50
problem
literature
convergence results
articles
https://doi.org/10.1186/s13662-022-03698-5
results
SP algorithm
Hilbert space
On some accelerated optimization algorithms based on fixed point and linesearch techniques for convex minimization problems with applications
applications
accelerated optimization algorithms
stepsize
conditions
weak convergence theorem
Mathematical Sciences
pub.1146355840
dimensions_id
Adisak
Hanjing
Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand
Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand
Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand
Suantai
Suthep
Springer Nature
Advances in Continuous and Discrete Models
2731-4235
1687-1839
Department of Mathematics, Faculty of Science, Nakhon Phanom University, Nakhon Phanom, Thailand
Department of Mathematics, Faculty of Science, Nakhon Phanom University, Nakhon Phanom, Thailand
doi
10.1186/s13662-022-03698-5
Department of Science and Mathematics, Rajamangala University of Technology Isan Surin Campus, Surin, Thailand
Department of Science and Mathematics, Rajamangala University of Technology Isan Surin Campus, Surin, Thailand
Pure Mathematics
Springer Nature - SN SciGraph project
Yatakoat
Pornsak
2022