Editorial: A special issue on vector and set optimization in applications
Bibliographic record
Abstract
Vector and set optimization represent modern research directions in applied mathematics with important applications, especially in economics, financial mathematics, risk theory, and medicine.The objective of this special issue is to present modern research results in the fields of vector and set optimization including their applications.It is a great pleasure for us to briefly introduce the contributions for our special issue.This special issue starts with the contribution "Vectorial penalisation in vector optimisation in real linear-topological spaces" by C. Günther, E. Köbis, P. Schmölling, and C. Tammer.This paper presents a vectorial penalization approach for vector optimization problems in which the vector-valued objective function acts between real topological-linear spaces, where the image space is partially ordered by a pointed convex cone.The penalization approach replaces the original constrained vector optimization problem (with not necessarily convex feasible set) by two unconstrained vector optimization problems, where in one of the two problems a penalization term with respect to the original feasible set is added to the vector objective function.For deriving the main results, a generalized convexity (quasiconvexity) notion for vector functions is supposed.The paper "Further results on quasi efficient solutions in multiobjective optimization" by César Gutiérrez Vaquero, is dealing with quasi efficient solutions of a vector optimization problem.The objective function is acting between finite dimensional spaces and the ordering in the image space is defined by a pointed convex cone.Several new concepts of quasi efficient solutions are introduced and their basic properties are derived in this setting.Linear scalarization results are discussed that characterize the introduced quasi efficient solutions by solutions of scalar optimization problems for convex problems.The contribution "Convergence rates for nonlinear inverse problems of parameter identification using Bregman distances" by D. N. Hao, A. A. Khan, and S. Reich is devoted to the establishment of new convergence rates for the nonlinear inverse problem concerning the identification of variable parameters in an abstract variational problem.The authors employ the energy least squares and output least squares methods to discuss the inverse problem in an optimization framework.In terms of the re-nowned Bregman distance associated with a convex regularizer, the convergence rates are given.The paper "On set-valued discrete dynamical systems" by E. Hernandez and J. Peran deals with set-valued discrete dynamical systems with the aim of establishing a general framework
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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 | 0.015 |
| Meta-epidemiology (narrow) | 0.005 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.005 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.003 | 0.002 |
| Scholarly communication | 0.010 | 0.005 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.011 | 0.014 |
| Insufficient payload (model declined to judge) | 0.041 | 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".