A special issue on the theory and numerical methods for vector optimization problems with respect to variable domination structures
Bibliographic record
Abstract
The objective of this special issue is to present advances in the applications of variable domination structures in vector optimization from a theoretical and numerical perspective.Vector and set optimization with variable domination structures is a growing and expanding field of applied mathematics with applications in medicine, imaging science, psychology, behavioural sciences, logistics, and uncertain programming.Hereby, one deals with optimization problems where the domination structure is given by a set-valued map acting between abstract or finite dimensional spaces.The concept of variable domination structures can be viewed as a generalization of the solution concept with fixed domination structures in multi-objective decisionmaking problems.It is our great pleasure to discuss the contributions of the finally selected papers below.This special issue starts with the contribution "A Steepest Descent-like Method for Vector Optimization Problems with Variable Domination Structure" by G. Bouza and Chr.Tammer.This paper proposes a steepest descent-like method for computing nondominated solutions of smooth uncon-strained vector optimization problems with variable domination structure.The authors demonstrate that every accumulation point of the generated sequence satisfies a first order necessary condition.The consequences of this fact are discussed in the convex case.In the paper "Approximate Efficiency in Set-Valued Optimization with Variable Order" by M. Durea, E.-A.Florea, D.-E.Maxim, and R. Strugariu, the authors study constrained set-valued optimization problems with variable order.The aim of this contribution is to deduce conditions for stability of minima of such problems at the perturbations of the objective map and the set of constraints, and furthermore, to study certain possibilities of recovering optimization problems with fixed order.The results are employed in order to derive optimality conditions for constrained set-valued optimization problems with variable order.Four types of cone enlargements are the main tools for deriving the results.The work "Optimal Payoffs for Directionally Closed Acceptance Sets", authored by M. Marohn and Chr.Tammer, considers directionally closed acceptance sets in the linear space of capital positions.Assuming finitely many eligible assets, the decision maker of a financial institution has to decide how to invest into these assets to secure acceptability for the financial position, meaning that the resulting capital position belongs to the acceptance set.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.034 | 0.009 |
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".