A Newton method for uncertain multiobjective optimization problems with finite uncertainty sets
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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.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it