Modified forward-backward splitting method for split equilibrium, variational inclusion, and fixed point problems
Bibliographic record
Abstract
In the recent time, the problem of finding common solutions of fixed point problems (FPPs) of nonlinear mappings and optimization problems (OPs) has received great research attention due to its potential applications to mathematical models whose constraints can be expressed as the FPPs and OPs. In this paper, we study the problem of finding a common solution of a split equilibrium problem (SEP), a variational inclusion problem (VIP) and the FPP with a finite family of multivalued demicontractive mappings. We propose a new inertial iterative method, which employs the forward-backward splitting technique together with the viscosity method for approximating the solution of the problem in Hilbert spaces. The proposed method uses variable step sizes, which do not depend on the norm of the bounded linear operator. We prove strong convergence results under some mild conditions. Finally, we present some numerical experiments to demonstrate the efficiency and applicability of the proposed method. Our result improves and extends several existing results in the current literature in this direction.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".