A Newton method for uncertain multiobjective optimization problems with finite uncertainty sets
Bibliographic record
Abstract
In this study, we investigate an uncertain multiobjective optimization problem through a setvalued optimization problem, and introduce a Newton method to find robust weakly efficient points of the considered uncertain optimization problem.We assume that the problem under consideration has uncertainty only in the objective function, and the involved uncertainty set is of finite cardinality.Also, for each uncertain scenario, the components of the objective function of the problem are assumed to be twice continuously differentiable and locally strong convex.Utilizing the concept of a partition set from set optimization, we formulate a class of vector optimization problems to solve the formulated set optimization problem pertaining to the considered uncertain multiobjective optimization.We derive a Newton method to solve this class of vector optimization problems that facilitates generating a sequence of points whose any limit point is a weakly robust efficient solution of the considered problem.The proposed method is found to have a local superlinear convergence rate under standard hypotheses with a regularity condition.Additionally, assuming Lipschitz continuity of the Hessian of the objective function for all scenarios, we show local quadratic convergence of the method.Finally, we provide numerical examples to discuss and illustrate the performance of the proposed method.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".