Editorial: A special issue on mathematical optimization and applications
Bibliographic record
Abstract
The theory of mathematical optimization is concerned with the study of the minimization of mathematical functions.Usually, the optimization variables are subject to some side conditions or constraints.Optimization methods are now under spotlight of research due to their great utility in diverse areas, such as finance, engineering, and statistics.In particular, machine learning has been in recent years in the forefront of significant research activities.A key component of these research developments is the interplay with optimization methods.This special issue focuses on recent research trends on the methods of mathematical optimization and their applications, aiming to push the developments of mathematical optimization for real-world problems.This special issue covers several hot topics.Details are presented below.The paper "A scalable sphere-constrained magnitude-sparse SAR imaging" by M. Jiang, J. Qu, J. Ding, and J. Liang, establishes a sphere-constrained magnitude-sparsity SAR imaging model to enhance the SAR imaging quality with high efficiency.This paper also proposes a non-convex non-smooth optimization method, which can be accelerated by stochastic average gradient acceleration to be scalable with large-scale problems.Numerical experiments are conducted with point-target and extended-target simulations.In the contribution, entitled "Quasi-subgradient methods with Bregman distance for quasiconvex feasibility problems" by Y. Hu, J. Li, Y. Liu, and C.K.W. Yu, a quasi-convex feasibility problem was studied.A unified framework of Bregman quasi-subgradient methods was presented for solving the problem.The convergence theory, including the global convergence, iteration complexity, and convergence rates, of the Bregman quasi-subgradient methods with several general control schemes was obtained.L. Liu and S.Y.Cho, in "A Bregman projection algorithm with self adaptive step sizes for split variational inequality problems involving non-Lipschitz operators", discussed a split variational inequality problem governed by pseudomonotone and not necessarily Lipschitz continuous operators.They introduced a Bregman projection algorithm and presented the convergence analysis in the framework of Hilbert spaces.They also provided some numerical experiments to support their convergence theorems.The paper "The level-set subdifferential error bound via Moreau envelopes" by Y. Wang, S. Li, M. Li, and X. Li is devoted to the behaviour of the level-set subdifferential error bound via Moreau envelopes under suitable assumptions.This paper provides an example that the Moreau
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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 | 0.004 | 0.016 |
| Meta-epidemiology (narrow) | 0.005 | 0.001 |
| Meta-epidemiology (broad) | 0.005 | 0.005 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.003 | 0.002 |
| Scholarly communication | 0.010 | 0.005 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.010 | 0.014 |
| Insufficient payload (model declined to judge) | 0.053 | 0.035 |
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".