Solving an uncertain quadratic multiobjective optimization problem using Newton’s descent method via a robust optimization approach
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Bibliographic record
Abstract
In this paper, we develop a Newton's descent method (NDM) for an uncertain quadratic multiobjective optimization problem (UQMOP).To accomplish this, we utilize a minimum of the objective wise worst case (OWWC) type robust counterpart (RC) of the UQMOP.The resulting RC is a nonsmooth multiobjective optimization problem (MOP).Our approach involves constructing a sub-problem to determine Newton's descent direction (NDD) for the RC.An Armijo-type inexact line search (AILS) technique is employed to identify an appropriate step length.Using NDD and step length, we formulate a Newton's descent algorithm (NDA) for the RC.Under some assumptions, we establish the convergence of NDA for the RC.Under specific assumptions, we demonstrate that the sequence defined by the NDA converges rapidly to the solution, exhibiting both superlinear and quadratic rate of convergence.Finally, we assess the efficacy of NDA by conducting a comparative analysis with the weighted sum method via various numerical problems.We obtain the non-dominated Pareto front for both methods, which support our 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 | 0.004 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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