A Special Issue on Recent Trends in Numerical Algorithms and Their Applications
Bibliographic record
Abstract
In the modern information age, numerical algorithms receive much attention than ever before due to their wide applications in applied mathematics, management science, computer science, medicine, economics, and other engineering fields.This special issue focuses on the recent trends in various numerical algorithms and their applications.The contributions to this special issue include optimization methods, models, and algorithms that deal with various pure and applied problems emerged in the last decades.This special issue is comprised of nine articles whose contributions are as follows: K. Guo and C. Zhu, in the paper "On the linear convergence of a Bregman proximal point algorithm," studied a Bregman proximal point algorithm for a convex optimization problem.They analyzed the linear convergence rate and establish the linear convergence of the iterative sequence of the algorithm.In the paper "Multiple-sets split quasi-convex feasibility problems: Adaptive subgradient methods with convergence guarantee," Y. Hu, G. Li, M. Li, and C.K.W. Yu considered a multiple-sets split quasiconvex feasibility problem (MSSQFP), which is to find a point such that itself and its image under a linear transformation fall within two families of sublevel sets of quasi-convex functions in the space and the image space, respectively.A unified framework of the adaptive subgradient methods with general control schemes was proposed to solve the MSSQFP.They established the quantitative convergence theory of adaptive subgradient methods with several general control schemes.An interesting finding was disclosed by the iteration complexity results that the stochastic control enjoys both advantages of low computational cost requirement and low iteration complexity.The paper "Multi-objective optimization of a nonlinear batch time-delay system with minimum system sensitivity" by L. Wang et al. focuses a nonlinear time-delay dynamic (NTDD) system with uncertain time-delay in batch culture of glycerol bioconversion to the 1, 3-propanediol (1, 3-PD) induced by Klebsiella pneumoniae.They designed an optimization scheme for the NTDD system with the aim of balancing two competing objectives: (i) system cost (the relative error between experimental data and the output of the mathematical model); (ii) system sensitivity (the variation of the system cost with respect to uncertain time-delay).A multi-objective optimization problem (MOOP) governed by the NTDD system was converted into a sequence of single-objective optimization problems (SOOCPs) by using convex c 2022 Journal of Nonlinear and Variational Analysis to be suitable for the multikernel-based approximation method, including the global convergence and the locally superlinear convergence.They also discussed some problems behind the choice of the truncated length M and the low-rank approximation.In conclusion, we express our most sincere gratitude to all the authors and the referees who contributed to this special issue, and we hope that the readers will enjoy it.
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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 | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.006 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.066 | 0.024 |
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".